Question 1: Palette 1/249

Advance Online April 2019 MCQ

Ship A is sailing towards north-east with velocity $\vec{v}=30\hat{i}+50\hat{j}$ kmhr $^{-1}$ where $\hat{i}$ points east and $\hat{j}$ , north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 kmhr $^{-1}$ . A will be at minimum distance B in

A

2.2 hr

B

4.2 hr

C

3.2 hr

D

2.6 hr

Question 2: Palette 2/249

Advance Online April 2019 MCQ

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)
(I)

(II)

(III)

(IV)

A

(I)

B

(I), (II), (III)

C

(I), (II), (IV)

D

(II), (III)

Question 3: Palette 3/249

Advance Online April 2019 MCQ

The stream of a river is flowing with a speed of $2 \, kmh^{-1}$ . A swimmer can swim at a speed of $4 \, kmh^{-1}$ . What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

A

$60^{\circ}$

B

$90^{\circ}$

C

$150^{\circ}$

D

$120^{\circ}$

Question 4: Palette 4/249

Advance Online April 2019 MCQ

The position vector of a particle changes with time according to the relation $\vec{r}(t) = 15t^2\hat{i} + (4 - 20t^2)\hat{j}$ . What is the magnitude of the acceleration at $t = 1$ ?

A

50

B

100

C

40

D

25

Question 5: Palette 5/249

Advance Online April 2019 MCQ

The position of a particle as a function of time t, is given by $x(t) = at + bt^{2} - ct^{3}$ where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be

A

$a + \frac{b^{2}}{4c}$

B

$a + \frac{b^{2}}{3c}$

C

$a + \frac{b^{2}}{2c}$

D

$a + \frac{b^{2}}{c}$

Question 6: Palette 6/249

Advance Online April 2019 MCQ

A bullet of mass 20 g has an initial speed of $1 \, ms^{-1}$ , just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of $2.5 \times 10^{-2} \, N$ , the speed of the bullet after emerging from the other side of the wall is close to

A

$0.4 \, ms^{-1}$

B

$0.7 \, ms^{-1}$

C

$0.3 \, ms^{-1}$

D

$0.1 \, ms^{-1}$

Question 7: Palette 7/249

Advance Online April 2019 MCQ

A particle is moving with speed $v = b\sqrt{x}$ along positive x-axis. Calculate the speed of the particle at time $t = \tau$ (assume that the particle is at origin at t = 0).

A

$b^{2}\tau$

B

$\frac{b^{2}\tau}{4}$

C

$\frac{b^{2}\tau}{2}$

D

$\frac{b^{2}\tau}{\sqrt{2}}$

Question 8: Palette 8/249

Advance Online January 2019 MCQ

A particle is moving with a velocity $\vec{v} = k(y\hat{i} + x\hat{j})$ , where $K$ is a constant. The general equation for its path is

A

$y^{2} = x + \text{constant}$

B

$y = x^{2} + \text{constant}$

C

$y^{2} = x^{2} + \text{constant}$

D

$xy = \text{constant}$

Question 9: Palette 9/249

Advance Online January 2019 MCQ

In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed v more than that of car B. Both the cars start from rest and travel with constant acceleration $a_{1}$ and $a_{2}$ respectively. Then v is equal to

A

$\frac{a_{1}+a_{2}}{2}t$

B

$\frac{2a_{1}a_{2}}{a_{1}+a_{2}}t$

C

$\sqrt{2a_{1}a_{2}}t$

D

$\sqrt{a_{1}a_{2}}t$

Question 10: Palette 10/249

Advance Online January 2019 MCQ

The position co-ordinates of a particle moving in a 3-D coordinate system is given by $x = a \cos(\omega t)$ , $y = a \sin(\omega t)$ and $z = a \omega t$ . The speed of the particle is

A

$2a\omega$

B

$\sqrt{2}a\omega$

C

$\sqrt{3}a\omega$

D

$a\omega$

Question 11: Palette 11/249

Advance Online January 2019 MCQ

A particle starts from the origin at time $t = 0$ and moves along the positive $x$ -axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle time $t = 5 \, \text{s}$ ?

A

$9\mathrm{m}$

B

$6\mathrm{m}$

C

$10\mathrm{m}$

D

$3\mathrm{m}$

Question 12: Palette 12/249

Advance Online January 2019 MCQ

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction and (ii) in the opposite directions is

A

$\frac{25}{11}$

B

$\frac{5}{2}$

C

$\frac{11}{5}$

D

$\frac{3}{2}$

Question 13: Palette 13/249

Advance 2018 MCQ

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up

A

Velocity

B

Distance

C

Position

D

Velocity

Question 14: Palette 14/249

Advance Online 2018 MCQ

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively

A

112.5 m and 15 s

B

337.5 m and 25 s

C

225.5 m and 10 s

D

112.5 m and 22.5 s

Question 15: Palette 15/249

Advance Online 2018 MCQ

An automobile, travelling at $40 \, kmh^{-1}$ , can be stopped at a distance of $40 \, m$ by applying brakes. If the same automobile is travelling at $80 \, kmh^{-1}$ , the minimum stopping distance, in metres, is (assume no skidding)

A

100 m

B

75 m

C

160 m

D

150 m

Question 16: Palette 16/249

Advance Online 2018 MCQ

A man in a car at location Q on a straight highway is moving with speed v. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum?

A

$\frac{d}{2}$

B

$\frac{d}{\sqrt{3}}$

C

$\frac{d}{\sqrt{2}}$

D

$d$

Question 17: Palette 17/249

Advance 2017 MCQ

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity versus time?

A

B

C

D

Question 18: Palette 18/249

Advance Online 2017 MCQ

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?

A

B

C

D

Question 19: Palette 19/249

Advance Online 2017 MCQ

The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a

A

speed which is $\frac{3}{4}^{th}$ of that of the roller when the weight is 0.4 m above the ground.

B

constant speed.

C

decreasing speed.

D

increasing speed.

Question 20: Palette 20/249

Advance Online 2017 MCQ

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration $2 \, ms^{-2}$ and the car has acceleration $4 \, ms^{-2}$ . The car will catch up with the bus after a time of

A

$\sqrt{120}$ s

B

15 s

C

$10\sqrt{2}$ s

D

$\sqrt{110}$ s

Question 21: Palette 21/249

Advance 2015 MCQ

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of $10 \, ms^{-1}$ and $40 \, ms^{-1}$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take $g = 10 \, ms^{-2}$ ) (The figures are schematic and not drawn to scale)

A

B

C

D

Question 22: Palette 22/249

Advance 2014 MCQ

From a tower of height $H$ , a particle is thrown vertically upwards with a speed $u$ . The time taken by the particle, to hit the ground, is $n$ times that taken by it to reach the highest point of its path. The relation between $H$ , $u$ and $n$ is

A

$gH = (n - 2)u^2$

B

$2gH = n^2 u^2$

C

$gH = (n - 2)^2 u^2$

D

$2gH = nu^2 (n - 2)$

Question 23: Palette 23/249

Advance 2011 MCQ

An object moving with a speed of $6.25 \, ms^{-1}$ , is decelerated at a rate given by $\frac{dv}{dt} = -2.5\sqrt{v}$ , where v is the instantaneous speed. The time taken by the object, to come to rest, would be

A

1 s

B

2 s

C

4 s

D

8 s

Question 24: Palette 24/249

Advance 2010 MCQ

A particle is moving with velocity $\vec{v} = K(y\hat{i} + x\hat{j})$ where $K$ is a constant. The general equation for its path is

A

$y^{2} = x^{2} + \text{constant}$

B

$y = x^{2} + \text{constant}$

C

$y^{2} = x + \text{constant}$

D

$xy = \text{constant}$

Question 25: Palette 25/249

Advance 2009 MCQ

A particle has an initial velocity $3\hat{i} + 4\hat{j}$ and an acceleration of $0.4\hat{i} + 0.3\hat{j}$ . Its speed after 10 s is

A

10 units

B

$7\sqrt{2}$ units

C

7 units

D

8.5 units

Question 26: Palette 26/249

Advance JEE (Advanced) 2008 MCQ

Statement-I: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary. Statement-II: If the observer and the object are moving at velocities $v_{1}$ and $v_{2}$ , respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $v_{2} - v_{1}$ .

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 27: Palette 27/249

Advance IIT-JEE 2005 MCQ

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?

A

B

C

D

Question 28: Palette 28/249

Advance IIT-JEE 2004 MCQ

A small block slides without friction down an inclined plane starting from rest. Let $S_{n}$ be the distance travelled from time $t = n - 1$ to $t = n$ . Then $\frac{S_n}{S_{n+1}}$ is

A

$\frac{2n - 1}{2n}$

B

$\frac{2n + 1}{2n - 1}$

C

$\frac{2n - 1}{2n + 1}$

D

$\frac{2n}{2n + 1}$

Question 29: Palette 29/249

Advance IIT-JEE 2004 MCQ

A particle starts from rest. Its acceleration $(a)$ versus time $(t)$ is as shown in the figure. The maximum speed of the particle will be

A

$110\mathrm{ms}^{-1}$

B

$55\mathrm{ms}^{-1}$

C

$550\mathrm{ms}^{-1}$

D

$660\mathrm{ms}^{-1}$

Question 30: Palette 30/249

Advance 11-JEE 2000 MCQ

A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $\frac{1}{2} d$ . Neglecting subsequent motion and air resistance, its velocity $v$ varies with the height $h$ above the ground as

A

B

C

D

Question 31: Palette 31/249

Advance IIT-JEE 1999 MCQ

In 1.0 second a particle goes from point A to point B moving in a semi-circle of radius 1.0 metre (figure). The magnitude of the average velocity is

A

$3.14\mathrm{ms}^{-1}$

B

$2.0\mathrm{ms}^{-1}$

C

$1.0\mathrm{ms}^{-1}$

D

ZERO

Question 32: Palette 32/249

Advance IIT-JEE 1999 MSQ

The co-ordinates of a particle moving in a plane are given by $x = a \cos(pt)$ and $y = b \sin(pt)$ where a, $b (< a)$ and p are positive constants of appropriate dimensions. Then

A

the path of the particle is an ellipse.

B

the velocity and acceleration of the particle are normal to each other at $t = \frac{\pi}{2p}$ .

C

the acceleration of the particle is always directed towards the focus.

D

the distance travelled by the particle in time interval $t = 0$ to $t = \frac{\pi}{2p}$ is $a$ .

Question 33: Palette 33/249

Advance IIT-JEE 1993 MCQ

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t=0. At this instant of time, the horizontal component of its velocity is v. A bead Q of same mass as P is ejected from A at t=0 along the horizontal string AB, with a speed v. Friction between the bead and the string may be neglected. Let $t_{P}$ and $t_{Q}$ be the respective times taken by P and Q to reach the point B, then

A

$t_{P} < t_{Q}$

B

$t_{P}=t_{Q}$

C

$t_{P} > t_{Q}$

D

$\frac{t_{\mathrm{P}}}{t_{\mathrm{Q}}} = \frac{\text{length of arc } ACB}{\text{length of chord } AB}$

Question 34: Palette 34/249

Advance IIT-JEE 1993 MSQ

A particle of mass m moves on the x-axis as follows: it starts from rest at t=0 from the point x=0 and comes to rest at t=1 at the point x=1. No other information is available about its motion at intermediate time $\text{(0t1)}$ . If $\alpha$ denotes the instantaneous acceleration of the particle, then

A

$\alpha$ cannot remain positive for all $t$ in the interval $0 \leq t \leq 1$

B

$|\alpha|$ cannot exceed 2 at any point in its path

C

$|\alpha|$ must be $\geq 4$ at some point or points in its path

D

$\alpha$ must change sign during the motion but no other assertion can be made with the information given

Question 35: Palette 35/249

Advance IIT-JEE 1988 MCQ

A boat which has a speed of $5\mathrm{kmh}^{-1}$ in still water crosses a river of width $1\mathrm{km}$ along the shortest possible path in 15 minute. The velocity of the river water in $\mathrm{kmh}^{-1}$ is

A

1

B

3

C

4

D

$\sqrt{41}$

Question 36: Palette 36/249

Advance IIT-JEE 1983 MCQ

A river is flowing from west to east at a speed of 5 m per minute. A man on the south bank of the river, capable of swimming at 10 m per minute in still water wants to swim across the river to a point directly opposite in the shortest time. He should then swim in a direction

A

$$<br /> 6 0 ^ {\circ}<br /> $$west of north

B

$30^{\circ}$ east of north

C

$30^{\circ}$ west of north

D

$60^{\circ}$ east of north

Question 37: Palette 37/249

Advance IIT-JEE 1982 MCQ

In the arrangement shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed

A

$2U\cos \theta$

B

$\frac{U}{\cos\theta}$

C

$\frac{2U}{\cos\theta}$

D

$U \cos \theta$

Question 38: Palette 38/249

Advance IIT-JEE 1982 MCQ

A particle is moving Eastwards with a velocity of $5 \, ms^{-1}$ . In 10 s, the velocity changes to $5 \, ms^{-1}$ Northwards. The average acceleration in this time is

A

zero

B

$\frac{1}{\sqrt{2}} \, ms^{-2}$ towards North-East

C

$\frac{1}{\sqrt{2}} \, ms^{-2}$ towards North-West

D

$\frac{1}{2} \, ms^{-2}$ towards North

Question 39: Palette 39/249

Advance MCQ

A particle has an initial velocity of $9 \, ms^{-1}$ due east and a constant acceleration of $2 \, ms^{-2}$ due west. The distance covered by the particle in the fifth second of its motion is

A

0 m

B

0.5 m

C

2 m

D

20 m

Question 40: Palette 40/249

Advance MCQ

The velocity of a car travelling on a straight road is given by the equation $v = 9 + 8t - t^{2}$ where v is in metre per second and t in second. The instantaneous acceleration when t = 5 s is

A

$2 \, ms^{-2}$

B

$1 \, ms^{-2}$

C

$-1 \, ms^{-2}$

D

$-2 \, ms^{-2}$

Question 41: Palette 41/249

Advance MCQ

A racing car travelling at a constant speed has to pass through a horizontal turn where the radius of curvature of the road is 200 m. If the normal acceleration of the car cannot exceed 0.8 g where $g = 10 \, ms^{-2}$ , the maximum speed of the car without sliding can be

A

$36 \, kmh^{-1}$

B

$72 \, kmh^{-1}$

C

$144 \, kmh^{-1}$

D

$174 \, kmh^{-1}$

Question 42: Palette 42/249

Advance MCQ

Ball A is dropped from the top of a tower of height H. At the same instant ball B is thrown vertically upwards from the ground. When the balls collide, they are moving in opposite directions and the speed of A is twice the speed of B. The height from the ground where the collision happens is

A

$\frac{H}{4}$

B

$\frac{H}{3}$

C

$\frac{2H}{5}$

D

$\frac{2H}{3}$

Question 43: Palette 43/249

Advance MCQ

Wind is blowing at a harbour with a speed of $72 \, kmh^{-1}$ and the flag on the mast of a boat anchored at harbour flutters along the North-East direction. If the boat starts moving at a speed of $51 \, kmh^{-1}$ due North, the direction of the flag is (in approximation)

A

towards east

B

towards west

C

towards north

D

towards south

Question 44: Palette 44/249

Advance MCQ

Two bodies begin to fall freely from the same height but the second falls T second after the first. The time (after which the first body begins to fall) when the distance between the bodies equals L is

A

$$ \frac {T}{2} $$

B

$$ \frac {T}{2} + \frac {L}{g T} $$

C

$$ \frac {L}{g T} $$

D

$$ T + \frac {2 L}{g T} $$

Question 45: Palette 45/249

Advance MCQ

A particle is dropped from point A at a certain height from ground. It falls freely and passes through three points B, C and D with BC = CD. The time taken by the particle to move from B to C is 2 seconds and from C to D is 1 second. The time taken to move from A to B is

A

0.25 s

B

0.5 s

C

0.75 s

D

1.5 s

Question 46: Palette 46/249

Advance MCQ

A juggler maintains four balls in motion, making each of them to rise a height of 20 m from his hand. The time interval that he should maintain, for the proper distance between them $g = 10 \, ms^{-2}$ is

A

0.5 s

B

1 s

C

2 s

D

3 s

Question 47: Palette 47/249

Advance MCQ

A particle starts from rest at time $t = 0$ and undergoes acceleration $a$ as shown. The velocity as function of time during the interval 0 to 4 second is indicated in

A

B

C

D

Question 48: Palette 48/249

Advance MCQ

The slopes of the windscreen of two motor cars are $\beta_{1} = 30^{\circ}$ and $\beta_{2} = 15^{\circ}$ respectively. The cars have velocities $v_{1}$ and $v_{2}$ in the horizontal direction. If the hailstones appear to the drivers to be bounced by the windscreen of their respective cars in the vertical direction then $\frac{v_1}{v_2}$ (assuming that hailstones were falling on the cars vertically) is

A

3

B

1

C

$\frac{1}{3}$

D

$\frac{1}{9}$

Question 49: Palette 49/249

Advance MCQ

A person walks up a stationary escalator in time $t_1$ . If he remains stationary on the escalator, then he reaches up in time $t_2$ . The time it would take him to walk up the moving escalator is

A

$\frac{t_1 + t_2}{2}$

B

$t_1 + t_2$

C

$\sqrt{t_1 t_2}$

D

$\frac{t_1 t_2}{t_1 + t_2}$

Question 50: Palette 50/249

Advance MCQ

One stone is dropped from a tower from rest and simultaneously another stone is projected vertically upwards from the tower with some initial velocity. The graph of the distance, $s$ between the two stones varies with time $(t)$ as (before either stone hits the ground)

A

B

C

D

Question 51: Palette 51/249

Advance MCQ

Wind is blowing from the south at $10 \, ms^{-1}$ but to a cyclist it appears to be blowing from the east at $10 \, ms^{-1}$ . The cyclist has a velocity

A

$10\hat{i}-10\hat{j}$

B

$10\hat{i}+10\hat{j}$

C

$-10\hat{i}+10\hat{j}$

D

$-10\hat{i}-10\hat{j}$

Question 52: Palette 52/249

Advance MCQ

If a particle takes t second less and acquires a velocity of $v \, ms^{-1}$ more in falling through the same distance on two planets where the accelerations due to gravity are 2 g and 8 g respectively then

A

$v = 4gt$

B

$v = 5gt$

C

$v = 2gt$

D

$v = 16gt$

Question 53: Palette 53/249

Advance MCQ

Velocity versus displacement graph of a particle moving in a straight line is shown in figure. Corresponding acceleration versus velocity graph will be

A

B

C

D

Question 54: Palette 54/249

Advance MCQ

Passengers in the jet transport A flying east at a speed of $800 \, kmh^{-1}$ observe a second jet plane B that passes under the transport in horizontal flight. Although the nose of B is pointed in the $45^{\circ}$ north east direction, plane B appears to the passengers in A to be moving away from the transport at the $60^{\circ}$ angle as shown. The true velocity of B is

A

$586\mathrm{kmh}^{-1}$

B

$400\sqrt{2}\mathrm{kmh}^{-1}$

C

$717\mathrm{kmh}^{-1}$

D

$400\mathrm{kmh}^{-1}$

Question 55: Palette 55/249

Advance MCQ

A body falling freely from a tower of height h covers a distance of $\frac{7}{16}h$ during the last second of its motion. Then the height of tower is (Take $g = 10 \, ms^{-2}$ )

A

60 m

B

70 m

C

80 m

D

90 m

Question 56: Palette 56/249

Advance MCQ

The figure shows the displacement-time graph (a parabola) of a body. This graph indicates that the initial velocity, in $ms^{-1}$ and acceleration, in $ms^{-2}$ respectively are

A

80,40

B

40,80

C

80,32

D

32,16

Question 57: Palette 57/249

Advance MCQ

Acceleration of a particle is $a$ for a time $t$ . It is followed immediately by a retardation of $a$ for time $\frac{t}{2}$ . Consider this as one cycle. If initial velocity of particle is zero, then the displacement of the particle after $n$ such cycles in succession is

A

$\frac{n(3n + 4)}{8} at^2$

B

$\frac{n(n + 1)}{2} at^2$

C

$\frac{(n^2 + n + 1)}{4} at^2$

D

$nat^2$

Question 58: Palette 58/249

Advance MCQ

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at the lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal is

A

$\sqrt{u^{2}-2gL}$

B

$\sqrt{2gL}$

C

$\sqrt{u^{2}-gL}$

D

$\sqrt{2(u^{2}-gL)}$

Question 59: Palette 59/249

Advance MCQ

For a particle moving rectilinearly the displacement $x$ depends on time $t$ as $x = at^3 + bt^2 + ct + d$ . The ratio of its initial acceleration to its initial velocity depends

A

only on $a$ and $b$

B

only on $b$ and $c$

C

only on $a$ and $c$

D

only on $a$

Question 60: Palette 60/249

Advance MCQ

A self-propelled vehicle of mass m whose engine delivers constant power P has an acceleration $a = \frac{P}{mv}$ (assume that there is no friction). In order to increase its velocity from $v_{1}$ to $v_{2}$ , the distance it has to travel will be

A

$\frac{m}{3P}\big(v_2 - v_1\big)$

B

$\frac{m}{3P}\Big(v_2^2 - v_1^2\Big)$

C

$\frac{m}{3P}\Big(v_2^3 - v_1^3\Big)$

D

$\frac{3P}{m}\Big(v_2^2 - v_1^2\Big)$

Question 61: Palette 61/249

Advance MCQ

The motion of a body falling from rest in a resisting medium is described by the equation $\frac{dv}{dt} = a - bv$ where $a$ and $b$ are constants. The velocity at any time $t$ is

A

$v_{t} = \frac{a}{b}\left(1 - e^{-bt}\right)$

B

$v_{t} = \frac{b}{a} e^{-bt}$

C

$v_{t} = \frac{a}{b}\left(1 + e^{-bt}\right)$

D

$v_{t} = \frac{b}{a} e^{bt}$

Question 62: Palette 62/249

Advance MCQ

A parachutist drops freely from an airplane for 10 s before the parachute opens. He then descends with a uniform retardation of $2.5 \, ms^{-2}$ . If he bails out of the plane at a height of 2495 m and g is $10 \, ms^{-2}$ , his velocity on reaching the ground will be

A

$5 \, ms^{-1}$

B

$10 \, ms^{-1}$

C

$15 \, ms^{-1}$

D

$20 \, ms^{-1}$

Question 63: Palette 63/249

Advance MCQ

The nucleus of a helium atom travels along the axis of a straight hollow tube 4 m long. The tube is part of a particle accelerator. If the particle enters the tube with a speed of $1000 \, ms^{-1}$ and leaves at $9000 \, ms^{-1}$ , and assuming that the acceleration is uniform, the time the particle remains inside the tube is

A

$4 \times 10^{-3} \, s$

B

$8 \times 10^{-4} \, s$

C

$1 \times 10^{-4} \, s$

D

$8 \times 10^{-3} \, s$

Question 64: Palette 64/249

Advance MCQ

Two cars A and B start off to race with velocities $8 \, ms^{-1}$ and $4 \, ms^{-1}$ and travel in straight line with uniform accelerations $2 \, ms^{-2}$ and $4 \, ms^{-2}$ respectively. If they reach the final point at the same instant, then the length of the path is

A

24 m

B

32 m

C

48 m

D

16 m

Question 65: Palette 65/249

Advance MCQ

A particle is moving in $x - y$ plane with $y = \frac{x}{2}$ and $v_{x} = 4 - 2t$ . The displacement versus time graph of the particle would be

A

B

C

D

Question 66: Palette 66/249

Advance MCQ

A ball is thrown vertically upwards. It was observed at a height $h$ twice with a time interval $\Delta t$ . The initial velocity of the ball is

A

$\sqrt{8gh + g^2(\Delta t)^2}$

B

$\sqrt{8gh + \left(\frac{g\Delta t}{2}\right)^2}$

C

$\frac{1}{2}\sqrt{8gh + g^2(\Delta t)^2}$

D

$\sqrt{8gh + 4g^2(\Delta t)^2}$

Question 67: Palette 67/249

Advance MCQ

A point moves in $x - y$ plane according to the law $x = 5\sin (6t)$ and $y = 5(1 - \cos (6t))$ , where $x$ and $y$ are in metre. The distance traversed by the particle in $t = 4$ s is

A

$24\mathrm{m}$

B

$48\mathrm{m}$

C

$96\mathrm{m}$

D

$120\mathrm{m}$

Question 68: Palette 68/249

Advance MCQ

A particle moving with uniform acceleration along a straight line covers distances $a$ and $b$ in successive intervals of $p$ and $q$ second. The acceleration of the particle is

A

$\frac{pq(p + q)}{2(bp - aq)}$

B

$\frac{2(aq - bp)}{pq(p + q)}$

C

$\frac{2(ap - bq)}{pq(p + q)}$

D

$\frac{2(bp - aq)}{pq(p + q)}$

Question 69: Palette 69/249

Advance MCQ

The motion of a particle is defined by $x = a \cos(\omega t)$ and $y = a \sin(\omega t)$ . The acceleration of the particle is

A

$a\omega$

B

$a^{2}\omega$

C

$a\omega^{2}$

D

$\frac{a\omega^{2}}{2}$

Question 70: Palette 70/249

Advance MCQ

The figure shows the acceleration versus time graph of a train. If it starts from rest, the distance it travels before it comes to rest is

A

30 metre

B

26 metre

C

13 metre

D

40 metre

Question 71: Palette 71/249

Advance MCQ

A car A is going north east at $80 \, kmh^{-1}$ and another car B is going south east with a velocity of $60 \, kmh^{-1}$ . The velocity of A relative to B makes an angle with the north equal to

A

$\tan^{-1}\left(\frac{2}{7}\right)$

B

$\tan^{-1}\left(\frac{7}{2}\right)$

C

$\tan^{-1}(7)$

D

$\tan^{-1}\left(\frac{1}{7}\right)$

Question 72: Palette 72/249

Advance MCQ

A particle is moving along a circular path of radius 3 metre in such a way that the distance travelled measured along the circumference is given by $s = \frac{t^2}{2} + \frac{t^3}{3}$ . The acceleration of the particle when $t = 2$ second is

A

$1.3 \, \text{ms}^{-2}$

B

$3 \, \text{ms}^{-2}$

C

$10 \, \text{ms}^{-2}$

D

$13 \, \text{ms}^{-2}$

Question 73: Palette 73/249

Advance MCQ

A lead ball is dropped into a lake from the diving board 5 m above the water. In hits the water with a certain velocity and then sinks to the bottom with this same constant velocity. It reaches the bottom 5 s after it is dropped. The depth of the lake is (take $g = 10 \, ms^{-2}$ )

A

10 m

B

20 m

C

25 m

D

40 m

Question 74: Palette 74/249

Advance MCQ

A balloon starts rising from the ground with an acceleration of $1.25 \, ms^{-2}$ . After 8 s, a stone is released from the balloon. The stone will

A

cover a distance of 40 m

B

have a displacement of 50 m

C

reach the ground in 4 s

D

begin to move down after being released

Question 75: Palette 75/249

Advance MCQ

The velocity acquired by a body when it falls through a height h is v. If it further falls through a height x ( $x \ll h$ ), the increase in velocity is approximately

A

$\frac{vx}{2h}$

B

$\frac{2v}{xh}$

C

$\frac{2vx}{h}$

D

$\frac{v}{2xh}$

Question 76: Palette 76/249

Advance MCQ

An armoured car 2 m long and 3 m wide is moving at $10 \, ms^{-1}$ when a bullet hits it in a direction making an angle $\tan^{-1}\left(\frac{3}{4}\right)$ with the length of the car as seen by a stationary observer. The bullet enters one edge of the car at the corner and passes out at the diagonally opposite corner. Neglecting any interaction between the car and the bullet, the time for the bullet to cross the car is

A

0.20 s

B

0.15 s

C

0.10 s

D

0.50 s

Question 77: Palette 77/249

Advance MCQ

A time-velocity graph of two vehicles $P$ and $Q$ starting from rest at the same time is given in the figure. The statement that can be deduced correctly from the graph is

A

velocity of $Q$ is greater than that of $P$

B

acceleration of $P$ is increasing at a slower rate than that of $Q$

C

acceleration of $Q$ is greater than that of $P$

D

acceleration of $P$ is greater than that of $Q$

Question 78: Palette 78/249

Advance MCQ

A stone takes time $t$ to fall through a height $h$ . The increment in time when it falls further through a distance $x$ ( $x \ll h$ ) is

A

$\frac{xth}{2}$

B

$\frac{xt}{2}$

C

$\frac{xt}{2h}$

D

$\frac{2h}{xt}$

Question 79: Palette 79/249

Advance MCQ

The speed of an aeroplane at the instant it lands on a runway is $60 \, ms^{-1}$ . If the deceleration of the aeroplane is given as $a = -0.6 - 0.001 \, v^{2}$ , the distance that it covers on the runway before coming to a stop is

A

98 metre

B

450 metre

C

973 metre

D

1800 metre

Question 80: Palette 80/249

Advance MCQ

In a 100 metre race, a runner accelerates uniformly from the start to his maximum velocity in a distance of $4\mathrm{m}$ and runs the remaining distance at that velocity. If he finishes the race in 10.4 second, then his maximum velocity was

A

$10~\mathrm{ms}^{-1}$

B

$15~\mathrm{ms}^{-1}$

C

$20~\mathrm{ms}^{-1}$

D

$25~\mathrm{ms}^{-1}$

Question 81: Palette 81/249

Advance MCQ

The position of a particle is given by $\vec{r} = a\cos (\omega t)\hat{i} + a\sin (\omega t)\hat{j} + bt\hat{k}$ where $\omega = \frac{2\pi}{T}$ and $T$ is time period for one revolution of the particle following a helical path. The distance moved by the particle in one full turn of the helix is

A

$\frac{4\pi}{\omega}\sqrt{a^2 + b^2\omega^2}$

B

$\frac{2\pi}{\omega}\sqrt{a^2\omega^2 + b^2}$

C

$\frac{2\pi}{\omega}\sqrt{a^2 + b^2\omega^2}$

D

$\frac{4\pi}{\omega}\sqrt{a^2\omega^2 + b^2}$

Question 82: Palette 82/249

Advance MCQ

The graph in the figure shows the velocity of a body plotted as a function of time. The distance covered by the body in the first 12 s is

A

$360\mathrm{m}$

B

$240\mathrm{m}$

C

$285\mathrm{m}$

D

$500\mathrm{m}$

Question 83: Palette 83/249

Advance MCQ

A horizontal wind is blowing with a velocity $v$ towards north-east. A man starts running towards north with acceleration $a$ . The time after which man will feel the wind blowing towards east is

A

$\frac{v}{a}$

B

$\frac{\sqrt{2}v}{a}$

C

$\frac{v}{\sqrt{2}a}$

D

$\frac{2v}{a}$

Question 84: Palette 84/249

Advance MCQ

A graph between the square of the velocity of a particle and the distance s moved by the particle is shown in the figure. The acceleration of the particle in kilometre per hour square is

A

2250

B

225

C

-2250

D

-225

Question 85: Palette 85/249

Advance MCQ

The speed of a body moving in a straight line changes from $25 \mathrm{~ms}^{-1}$ to $10 \mathrm{~ms}^{-1}$ in 3 s at a constant rate.

A

during this time it travels 52.5 metre.

B

its acceleration is $5 \mathrm{~ms}^{-2}$ .

C

its acceleration is greatest at the beginning because it is going fastest at that time.

D

the distance travelled during an interval of 3 second cannot be calculated from the given data.

Question 86: Palette 86/249

Advance MCQ

A car covers the first half of the distance between two places at a speed of $40\mathrm{kmh}^{-1}$ and the second half at $60\mathrm{kmh}^{-1}$ . The average speed of the car is

A

$50\mathrm{kmh}^{-1}$

B

$42\mathrm{kmh}^{-1}$

C

$35\mathrm{kmh}^{-1}$

D

$48\mathrm{kmh}^{-1}$

Question 87: Palette 87/249

Advance MCQ

Rain, pouring down at an angle $\alpha$ with the vertical has a speed of $10\mathrm{ms}^{-1}$ . A girl runs against the rain with a speed of $8\mathrm{ms}^{-1}$ and sees that the rain makes an angle $\beta$ with the vertical, then relation between $\alpha$ and $\beta$ is

A

$\tan \alpha = \frac{8 + 10\sin\beta}{10\cos\beta}$

B

$\tan \beta = \frac{8 + 10\sin\alpha}{10\cos\alpha}$

C

$\tan \alpha = \tan \beta$

D

$\tan \alpha = \cot \beta$

Question 88: Palette 88/249

Advance MCQ

A smooth square platform ABCD is moving towards right with a uniform speed v. A particle is projected from A with speed 2v making an angle $\theta$ with AD so that it strikes the point B. Then $\theta$ equals

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$90^{\circ}$

Question 89: Palette 89/249

Advance MCQ

An express elevator can accelerate or decelerate with values whose magnitudes are limited to 0.4g. The elevator attains a maximum vertical speed of 400 metre per minute. The minimum time required by the elevator to start from rest from the 10th floor and to stop at the 30th floor, a distance 100 m apart is

A

1.67 s

B

16.7 s

C

167 s

D

1670 s

Question 90: Palette 90/249

Advance MCQ

A swimmer crosses a flowing stream of width $d$ to and fro in time $t_1$ . The time taken to cover the same distance up and down the stream is $t_{2}$ . If $t_{3}$ is the time the swimmer would take to swim a distance 2d in still water, then

A

$t_{3}=t_{1}+t_{2}$

B

$t_{3}^{2}=t_{1}t_{2}$

C

$t_{2}^{2}=t_{1}t_{3}$

D

$t_{1}^{2}=t_{2}t_{3}$

Question 91: Palette 91/249

Advance MCQ

A bullet loses $\frac{1}{20}$ of its velocity in passing through a plank. The least number of planks required to stop the bullet is

A

10

B

11

C

12

D

23

Question 92: Palette 92/249

Advance MCQ

A motorboat going down stream overcame a raft at a point A. 60 minute later it turned back and after some time passed the raft at a distance of 6 km from the point A. Assuming the duty of the engine to be constant, the flow velocity is

A

$3 \, kmh^{-1}$

B

$4 \, kmh^{-1}$

C

$5 \, kmh^{-1}$

D

$6 \, kmh^{-1}$

Question 93: Palette 93/249

Advance MCQ

A train travelling at $72 \, kmh^{-1}$ is checked by track repairs. It retards uniformly for 200 m covering next 400 m at constant speed and accelerates to $72 \, kmh^{-1}$ in a further distance of 600 m. If the time at constant lower speed is equal to the sum of the times taken in retarding and accelerating, the total time taken is

A

140 s

B

160 s

C

120 s

D

100 s

Question 94: Palette 94/249

Advance MCQ

For an airplane to take-off it accelerates according to the graph shown and takes 12 s to take-off from the rest position. The distance travelled by the airplane is

A

$21\mathrm{m}$

B

$210\mathrm{m}$

C

$2100\mathrm{m}$

D

$120\mathrm{m}$

Question 95: Palette 95/249

Advance MCQ

A body with constant acceleration travels 2 metre in the first 2 second and $2.2\mathrm{m}$ in the next 4 second. The velocity at the end of the seventh second from the start shall be

A

$0.1\mathrm{ms}^{-1}$

B

$0.2\mathrm{ms}^{-1}$

C

$0.5\mathrm{ms}^{-1}$

D

$1\mathrm{ms}^{-1}$

Question 96: Palette 96/249

Advance MCQ

A particle is released from rest from a tower of height $3h$ . The ratio of times to fall equal heights $h$ , i.e., $t_1: t_2: t_3$ is

A

$3: 2: 1$

B

$\sqrt{3}: \sqrt{2}: 1$

C

$1: (\sqrt{2} - 1): (\sqrt{3} - \sqrt{2})$

D

$9: 4: 1$

Question 97: Palette 97/249

Advance MCQ

Two particles A and B are thrown up simultaneously from the edge of a cliff with initial speeds v and 2v. Assuming that the particle A comes to rest immediately after striking the ground, the variation in relative position of the particle B with respect to the particle A with time, till both the stones strike the ground is plotted. This variation plot is

A

only linear

B

only parabolic

C

first parabolic then linear

D

first linear then parabolic

Question 98: Palette 98/249

Advance MCQ

A dog is chasing a cat who is running along a straight line at constant speed $u$ . The dog moves with a constant speed $v$ , always heading towards the cat. Initially i.e. at $t = 0$ , the velocities of dog and cat are perpendicular and the initial perpendicular distance between them is $l$ . The dog catches the cat at

A

$t = \frac{lv}{v^2 - u^2}$ for $v > u$

B

$t = \frac{lv}{u^2 - v^2}$ for $u > v$

C

$t = \frac{lv^2}{\sqrt{v^2 - u^2}}$ for $v > u$

D

$t = \frac{lv^2}{\sqrt{u^2 - v^2}}$ for $u > v$

Question 99: Palette 99/249

Advance MCQ

The acceleration is constant when the relationship between the

A

position coordinate $s$ and the square of the velocity $v$ is linear

B

position coordinate $s$ and the velocity $v$ is linear

C

position coordinate and the reciprocal of the velocity $v$ is linear

D

square of the position coordinate s and the velocity v is linear

Question 100: Palette 100/249

Advance MCQ

In travelling a distance of 3 kilometre between points A and D, a car is driven at $100 \, kmh^{-1}$ from A to B for t second and at $60 \, kmh^{-1}$ from C to D for t second. If the brakes are applied for 4 second between B and C to give the car a uniform deceleration, the value of t is

A

75.5 second

B

45.5 second

C

65.5 second

D

56.5 second

Question 101: Palette 101/249

Advance MCQ

A car is travelling on a straight road. The maximum velocity the car can attain is $24 \, ms^{-1}$ . The maximum acceleration and deceleration it can attain are $1 \, ms^{-2}$ and $4 \, ms^{-2}$ respectively. The shortest time the car takes to start from rest and come to rest in a distance of 200 metre is

A

22.4 second

B

33.6 second

C

11.2 second

D

5.6 second

Question 102: Palette 102/249

Advance MCQ

A person walks up a stalled escalator in 90 s. When standing on the same escalator, now moving, he is carried in 60 s. The time it would take him to walk up the moving escalator will be

A

36 s

B

18 s

C

72 s

D

27 s

Question 103: Palette 103/249

Advance MCQ

Two particles, A and B move with constant velocities $\vec{v}_A$ and $\vec{v}_B$ . Initially their radius vectors are $\vec{r}_A$ and $\vec{r}_B$ . For the particles to collide the four vectors must be interrelated as

A

$\vec{v}_A - \vec{v}_B = \vec{r}_A - \vec{r}_B$

B

$\vec{v}_A = \vec{v}_B$ and $\vec{r}_A = \vec{r}_B$

C

$\frac{\vec{v}_A + \vec{v}_B}{|\vec{v}_A + \vec{v}_B|} = \frac{\vec{r}_A + \vec{r}_B}{|\vec{r}_A + \vec{r}_B|}$

D

$\frac{\vec{v}_B - \vec{v}_A}{|\vec{v}_B - \vec{v}_A|} = \frac{\vec{r}_A - \vec{r}_B}{|\vec{r}_A - \vec{r}_B|}$

Question 104: Palette 104/249

Advance MCQ

The cone falling with a speed $v_{0}$ strikes and penetrates the block of packing material. The acceleration of the cone after impact is $a = g - cx^{2}$ , where c is a positive constant and x is the penetration distance. If the maximum penetration depth is $x_{m}$ . Then c equals

A

$\frac{2gx_m + v_0^2}{x_m^2}$

B

$\frac{2gx_m - v_0^2}{x_m^2}$

C

$\frac{6gx_m - 3v_0^2}{2x_m^3}$

D

$\frac{6gx_m + 3v_0^2}{2x_m^3}$

Question 105: Palette 105/249

Advance MCQ

Water drops fall at regular intervals from a roof. At an instant when a drop is about to leave the roof, the separations between 3 successive drops below the roof are in the ratio

A

1:2:3

B

1:4:9

C

1:3:5

D

1:5:13

Question 106: Palette 106/249

Advance MCQ

A particle has an initial velocity $\vec{u} = (6\hat{i} + 8\hat{j})\mathrm{ms}^{-1}$ and an acceleration of $\vec{a} = (0.8\hat{i} + 0.6\hat{j})\mathrm{ms}^{-2}$ . Its speed after $10\mathrm{s}$ is

A

$20\mathrm{ms}^{-1}$

B

$14\mathrm{ms}^{-1}$

C

$14\sqrt{2}\mathrm{ms}^{-1}$

D

$17\mathrm{ms}^{-1}$

Question 107: Palette 107/249

Advance MCQ

A car moves rectilinearly for 6 s with a velocity that varies with time as $|t-3|$ $ms^{-1}$ where t is in second. The total distance moved by the car is

A

3 m

B

6 m

C

9 m

D

12 m

Question 108: Palette 108/249

Advance MCQ

The V-t curves for two different particle motions are shown. The corresponding displacement time curves, taking S=0 when t=0 for both instances will be

A

B

C

D

Question 109: Palette 109/249

Advance MCQ

The acceleration of a train between two stations 2 kilometre apart is shown in the figure. The maximum speed of the train is

A

$30\mathrm{ms}^{-1}$

B

$60\mathrm{ms}^{-1}$

C

$90\mathrm{ms}^{-1}$

D

$120\mathrm{ms}^{-1}$

Question 110: Palette 110/249

Advance MCQ

The acceleration is constant when the relationship between

A

the square of the position coordinate $x$ and the velocity $v$ is linear

B

the position coordinate $x$ and the reciprocal of the velocity is linear

C

the position coordinate $x$ and velocity $v$ is linear

D

the position coordinate $x$ and the square of the velocity $v$ is linear

Question 111: Palette 111/249

Advance MCQ

A particle moves along a horizontal straight line with a velocity-time relationship as shown in figure. The total distance moved by the particle is

A

39 m

B

13 m

C

26 m

D

2.6 m

Question 112: Palette 112/249

Advance MCQ

A train moves from one station to another in 2 hour, and its speed during the motion is shown in the graph. The maximum acceleration during the journey is

A

$80\mathrm{kmh}^{-2}$

B

$160\mathrm{kmh}^{-2}$

C

$40\mathrm{kmh}^{-2}$

D

$60\mathrm{kmh}^{-2}$

Question 113: Palette 113/249

Advance MCQ

The wind appears to blow from the north to a man moving in the north-east direction. When he doubles his velocity the wind appears to move in the direction $\cot^{-1}(2)$ east of north. The actual direction of the wind is

A

$\sqrt{2} v$ towards east

B

$\frac{v}{\sqrt{2}}$ towards west

C

$\sqrt{2} v$ towards west

D

$\frac{v}{\sqrt{2}}$ towards east

Question 114: Palette 114/249

Advance MCQ

A man drives a car from Y towards X at speed $60 \, kmh^{-1}$ . A car leaves station X for station Y every 10 min. The distance between X and Y is 60 km. The car travels at speed $60 \, kmh^{-1}$ . A man drives a car from Y towards X at speed $60 \, kmh^{-1}$ . If he starts at the moment when first car leaves station X. The number of cars he would meet on route is

A

5

B

7

C

10

D

20

Question 115: Palette 115/249

Advance MCQ

A body falls from rest, in the last second of its fall, it covers half of the total distance. If $g$ is $9.8\mathrm{ms}^{-2}$ , then the total time of its fall is (in second)

A

2

B

$2 + \sqrt{2}$

C

$2 - \sqrt{2}$

D

$2 \pm \sqrt{2}$

Question 116: Palette 116/249

Advance MCQ

The motion of a body falling from rest in a resisting medium is described by the equation $\frac{dv}{dt} = A - Bv$ where $A$ and $B$ are constants. The velocity at any time $t$ is

A

$A(1 - e^{Bt})$

B

$ABte^{-t}$

C

$\frac{A}{B}(1 - e^{-Bt})$

D

$AB^2(1 - e^{-Bt})$

Question 117: Palette 117/249

Advance MCQ

In a car race, car A takes $t_{0}$ time less to finish than car B and passes the finishing point with a velocity $v_{0}$ more than car B. The cars start from rest and travel with constant accelerations $a_{1}$ and $a_{2}$ . Then the ratio $\frac{v_{0}}{t_{0}}$ is equal to

A

$\frac{a_{1}+a_{2}}{2}$

B

$\frac{a_{2}^{2}}{a_{1}}$

C

$\frac{a_{1}^{2}}{a_{2}}$

D

$\sqrt{a_{1}a_{2}}$

Question 118: Palette 118/249

Advance MCQ

A 2 m wide car is moving with a uniform speed of $8 \, ms^{-1}$ along the edge of a straight horizontal road. A pedestrian starts to cross the road with a speed v when the car is 12 m away from him. The minimum value of v for the pedestrian to cross the road safely is

A

$\frac{4}{3} \, ms^{-1}$

B

$\frac{3}{4} \, ms^{-1}$

C

$\frac{1}{2} \, ms^{-1}$

D

$\frac{1}{6} \, ms^{-1}$

Question 119: Palette 119/249

Advance MCQ

In PROBLEM 81, if $\theta$ is the angle made by the velocity of the pedestrian with the road then

A

$\tan \theta = 2$

B

$\tan \theta = \frac{1}{6}$

C

$\tan \theta = 6$

D

$\tan \theta = \frac{1}{2}$

Question 120: Palette 120/249

Advance MCQ

In PROBLEM 81, the time to cross the moving vehicle safely is

A

$\frac{24}{37}\mathrm{s}$

B

$\frac{37}{24}\mathrm{s}$

C

$\frac{24}{49}\mathrm{s}$

D

$\frac{3}{2}\mathrm{s}$

Question 121: Palette 121/249

Advance MCQ

A proton in a cyclotron moves in a circle of radius 0.8 metre at a speed of $10^{7} \mathrm{~ms}^{-1}$ . The acceleration of the proton and acceleration due to gravity have a ratio of approximately

A

$10^{10}$

B

$10^{11}$

C

$10^{13}$

D

$10^{14}$

Question 122: Palette 122/249

Advance MCQ

Two particles are released from the same height at an interval of 1 s. How long after the first particle begins to fall will the two particles be 10 m apart. $\left(g=10\ \mathrm{ms}^{-2}\right)$

A

1.25 s

B

1.5 s

C

2 s

D

2.5 s

Question 123: Palette 123/249

Advance MCQ

A particle thrown down from the top of a tower takes time $t_1$ to reach the ground. It takes time $t_2$ if thrown from the same point with the same speed in the upward direction. The time taken by it to fall freely to the ground from the top of tower is

A

$\frac{1}{2}(t_1 + t_2)$

B

$\frac{1}{2}(t_1 - t_2)$

C

$\frac{t_1t_2}{t_1 + t_2}$

D

$\sqrt{t_1t_2}$

Question 124: Palette 124/249

Advance MCQ

The acceleration-velocity graph of a particle moving rectilinearly is as shown in figure. Then slope of velocity-displacement graph must be

A

increasing linearly

B

decreasing linearly

C

a constant

D

increasing parabolically

Question 125: Palette 125/249

Advance MCQ

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $v$ and other with a uniform acceleration $a$ . If $\alpha$ is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by

A

$\frac{v}{a}\sin\alpha$

B

$\frac{v}{a}\cos\alpha$

C

$\frac{v}{a}\tan\alpha$

D

$\frac{v}{a}\cot\alpha$

Question 126: Palette 126/249

Advance MCQ

In PROBLEM 88, the least value of relative velocity is

A

$v \sin \alpha$

B

$v \cos \alpha$

C

$v \tan \alpha$

D

$v \cot \alpha$

Question 127: Palette 127/249

Advance MCQ

A body dropped from a certain height attains the same velocity as another falling with an initial velocity u from a height h below the first body. If g is the acceleration due to gravity, then

A

$u = \sqrt{gh}$

B

$u = 2\sqrt{gh}$

C

$u = \sqrt{2gh}$

D

$u = \sqrt{\frac{gh}{2}}$

Question 128: Palette 128/249

Advance MCQ

Two objects move uniformly toward each other. They get closer by 4 metre each second but when they move uniformly in the same direction, with the same speeds, they get 4 metre closer every 10 second. The speeds of the two objects are

A

$2.2 \mathrm{~ms}^{-1}$ and $1.8 \mathrm{~ms}^{-1}$

B

$1.1 \mathrm{~ms}^{-1}$ and $1.8 \mathrm{~ms}^{-1}$

C

$22 \mathrm{~ms}^{-1}$ and $18 \mathrm{~ms}^{-1}$

D

$1.7 \mathrm{~ms}^{-1}$ and $2.1 \mathrm{~ms}^{-1}$

Question 129: Palette 129/249

Advance MCQ

A body falls freely under gravity. The distance travelled by it in the last second of its journey equals the distance travelled by it in the first three seconds of its free fall. The total time taken by the body to reach the ground is

A

5 s

B

8 s

C

12 s

D

15 s

Question 130: Palette 130/249

Advance MCQ

Six persons are initially at the six corners of a hexagon of side $a$ . Each person now moves with a uniform speed $v$ in such a manner that 1 is always directed towards 2, 2 towards 3, 3 towards 4 and so on. The time after which they meet is

A

$\frac{2a}{v}$

B

$\frac{a}{v}$

C

$\frac{2a}{3v}$

D

$\frac{a}{2v}$

Question 131: Palette 131/249

Advance MCQ

Velocity versus displacement graph of a particle moving in a straight line is as shown in figure. The acceleration of the particle is

A

constant

B

increases parabolically with $x$

C

increases linearly with $x^2$

D

increases linearly with $x$

Question 132: Palette 132/249

Advance MCQ

The acceleration time graph of a particle moving in a straight line is as shown in figure. The velocity of the particle at time t=0 is $2 \, ms^{-1}$ . The velocity after 2 second will be

A

$2\mathrm{ms}^{-1}$

B

$4\mathrm{ms}^{-1}$

C

$6\mathrm{ms}^{-1}$

D

$8\mathrm{ms}^{-1}$

Question 133: Palette 133/249

Advance MCQ

A ball is thrown vertically up with a speed of $20 \, ms^{-1}$ . It is caught on its way down 5 m above the point from where it was thrown. The time lapse between the throw and the catch is

A

1.9 s

B

3.8 s

C

8.3 s

D

1.2 s

Question 134: Palette 134/249

Advance MCQ

Two particles start moving from the same point along the same straight line. The first moves with constant velocity $2v$ and the second with constant acceleration $a$ . During the time that elapses before the second catches the first, the greatest distance between the particles is

A

$\frac{v^2}{a}$

B

$\frac{v^2}{2a}$

C

$\frac{2v^2}{a}$

D

$\frac{v^2}{4a}$

Question 135: Palette 135/249

Advance MCQ

Starting from rest a particle moves in a straight line with acceleration $a=\left[2+|t-2|\right]ms^{-2}$ . Velocity of particle at the end of 4 s will be

A

$8\ ms^{-1}$

B

$12\ ms^{-1}$

C

$16\ ms^{-1}$

D

$20\ ms^{-1}$

Question 136: Palette 136/249

Advance MCQ

A body moving rectilinearly traversed one third of the total distance with a velocity $4 \, ms^{-1}$ . The remaining part of the distance was covered with a velocity $2 \, ms^{-1}$ for half the time and with velocity $6 \, ms^{-1}$ for the other half of time. The mean velocity averaged over the whole time of motion is

A

$5 \, ms^{-1}$

B

$4.5 \, ms^{-1}$

C

$3.5 \, ms^{-1}$

D

$4 \, ms^{-1}$

Question 137: Palette 137/249

Advance MCQ

A, B, C and D are four collinear points such that AB = BC = CD. If the average value of velocities between A and B, C and D are $12 \, ms^{-1}$ and $20 \, ms^{-1}$ respectively, then the value of average velocity between B and C if the body moves with uniform acceleration throughout is

A

$16 \, ms^{-1}$

B

$14 \, ms^{-1}$

C

$\left(1+\sqrt{241}\right)\mathrm{ms}^{-1}$

D

$8 \, ms^{-1}$

Question 138: Palette 138/249

Advance MCQ

A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is 4 cm and that of iron plate is 2 cm. A bullet fired goes through the wood first and then penetrates 1 cm into iron. A similar bullet fired with the same velocity from opposite direction goes through iron first and then penetrates 2 cm into wood. If $a_{1}$ and $a_{2}$ be the retardations offered to the bullet by wood and iron plates respectively then

A

$a_{1}=2a_{2}$

B

$a_{2}=2a_{1}$

C

$a_{1}=a_{2}$

D

Data Insufficient

Question 139: Palette 139/249

Advance MCQ

A ball is thrown from the top of a tower of height 80 metre with a horizontal velocity of $30\mathrm{ms}^{-1}$ . The velocity with which it strikes the level ground is

A

$20\mathrm{ms}^{-1}$

B

$50\mathrm{ms}^{-1}$

C

$80\mathrm{ms}^{-1}$

D

$100\mathrm{ms}^{-1}$

Question 140: Palette 140/249

Advance MCQ

A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height $\frac{1}{2}d$ . Neglecting subsequent motion and air resistance, its velocity v varies with the height h above the ground as

A

B

C

D

Question 141: Palette 141/249

Advance MCQ

A ball is dropped from the roof of a tower of height h. The total distance covered by it in the last second of its motion is equal to the distance covered by it in first three seconds. The value of h in meters is $\left(g=10\ \mathrm{ms}^{-2}\right)$

A

80

B

100

C

125

D

200

Question 142: Palette 142/249

Advance MCQ

A stone falls freely from a point O. It passes through the points P, Q, R,.....such that OP, OQ, OR, ..... are in geometric progression. Then velocities of stone at P, Q, R, .....are in

A

arithmetic progression

B

geometric progression

C

harmonic progression

D

logarithmic mean

Question 143: Palette 143/249

Advance MCQ

A particle projected vertically upwards attains a maximum height $H$ . If the ratio of the times to attain a height $h$ ( $h < H$ ) is $\frac{1}{3}$ then

A

$4h = 3H$

B

$3h = 4H$

C

$3h = H$

D

$4h = H$

Question 144: Palette 144/249

Advance MCQ

The velocity of a boat in still water is $\eta$ times less than the velocity of flow of the river ( $\eta > 1$ ). The angle with the stream direction at which the boat must move to minimise drifting is

A

$\sin^{-1}\left(\frac{1}{\eta}\right)$

B

$\cot^{-1}\left(\frac{1}{\eta}\right)$

C

$\frac{\pi}{2} + \sin^{-1}\left(\frac{1}{\eta}\right)$

D

$\frac{\pi}{2} + \cot^{-1}\left(\frac{1}{\eta}\right)$

Question 145: Palette 145/249

Advance MCQ

Sachin (S) hits a ball along the ground with a speed $u$ in a direction which makes an angle $30^{\circ}$ with the line joining him and the fielder Prem (P). Prem runs to intercept the ball with a speed $\frac{2u}{3}$ . At what angle $\theta$ should he run to intercept the ball?

A

$\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$

B

$\sin^{-1}\left(\frac{2}{3}\right)$

C

$\sin^{-1}\left(\frac{3}{4}\right)$

D

$\sin^{-1}\left(\frac{4}{5}\right)$

Question 146: Palette 146/249

Advance MSQ

A particle moves with an initial velocity $v_0$ and retardation $\alpha v$ , where $v$ is its velocity at any time $t$ . If $\log_e(2) = 0.7$ , then which of the following statement(s) is/are correct?

A

The particle will cover a total distance $\frac{v_0}{\alpha}$ .

B

The particle will come to rest after time $\frac{1}{\alpha}$ .

C

The particle will continue to move for a very long time.

D

The velocity of the particle will become $\frac{v_0}{2}$ after time $\frac{7}{10\alpha}$ .

Question 147: Palette 147/249

Advance MSQ

Average velocity of a particle moving in a straight line, with constant acceleration a and initial velocity u and final velocity v in first t second is

A

$$ \frac {u + v}{2} $$

B

$$ u + a t $$

C

$$ \frac {1}{2} (u + a t) $$

D

$$ u + \frac {1}{2} a t $$

Question 148: Palette 148/249

Advance MSQ

The velocity of a particle moving along a straight line increases according to the linear law $v = v_{0} + kx$ , where k is a constant. Then

A

the acceleration of the particle is $k(v_{0} + kx)$

B

the particle takes a time $\frac{1}{k}\log_e\left(\frac{v_1}{v_0}\right)$ to attain a velocity $v_{1}$ .

C

velocity varies linearly with displacement with slope of velocity displacement curve equal to k.

D

data is insufficient to arrive at a conclusion.

Question 149: Palette 149/249

Advance MSQ

A rod of length l leans by its upper end against a smooth vertical wall, while its other end leans against the floor. The end that leans against the wall moves uniformly downward. Then the

A

other end moves uniformly forward with speed v.

B

other end moves with a speed whose value decreases with increase in $y$ and vanishes at $y = 0$ .

C

other end moves with a speed whose value decreases with decrease in $y$ and vanishes at $y = 0$ .

D

other end moves such that the ratio $\frac{v_x}{v}$ equals $\frac{y}{\sqrt{l^2 - y^2}}$ .

Question 150: Palette 150/249

Advance MSQ

For a particle moving in a plane, if $\vec{v}$ and $\vec{a}$ be the instantaneous velocity and acceleration, then rate of change of speed, $\frac{dv}{dt}$ , of the particle equal(s)

A

$|\vec{a} |$

B

the component of $\vec{a}$ perpendicular to $\vec{v}$

C

$\frac{\vec{a} \cdot \vec{v}}{v}$

D

the projection of $\vec{a}$ along $\vec{v}$

Question 151: Palette 151/249

Advance MSQ

The position of a particle travelling along x-axis is given by $x_{t}=t^{3}-9t^{2}+6t$ where $x_{t}$ is in cm and t is in second. Then

A

the body comes to rest firstly at $(3-\sqrt{7})$ s and then at $(3+\sqrt{7})$ s.

B

the total displacement of the particle in travelling from the first zero of velocity to the second zero of velocity is zero.

C

the total displacement of the particle in travelling from the first zero of velocity to the second zero of velocity is -74 cm.

D

the particle reverses its velocity at $(3-\sqrt{7})$ s and then at $(3+\sqrt{7})$ s and has a negative velocity for $(3-\sqrt{7}) < t < (3+\sqrt{7})$

Question 152: Palette 152/249

Advance MSQ

A particle, starting from rest is first accelerated for time $t_{1}$ with constant acceleration $a_{1}$ and then stops in time $t_{2}$ with constant retardation $a_{2}$ . Let $v_{1}$ be the average velocity in this case and $s_{1}$ the total displacement. Now, the same particle, starting again from rest is accelerated for the same time $t_{1}$ with constant acceleration $2a_{1}$ and finally comes to rest with constant retardation $a_{2}$ in time $t_{3}$ . If $v_{2}$ is the average velocity in this case and $s_{2}$ the total displacement. Then

A

$s_{2}=2s_{1}$

B

$2s_{1} < s_{2}<4s_{1}$

C

$v_{2}=2v_{1}$

D

$2v_{1} < v_{2} < 4v_{1}$

Question 153: Palette 153/249

Advance MSQ

A particle moves with an initial velocity $v_{0}$ and retardation $\alpha v$ , where $v$ is velocity at any instant $t$ . Then

A

the particle will cover a total distance $\frac{v_0}{\alpha}$ .

B

the particle continues to move for a long time span.

C

the particle attains a velocity $\frac{1}{2} v_0$ at $t = \frac{1}{\alpha}$ .

D

the particle comes to rest at $t = \frac{1}{\alpha}$ .

Question 154: Palette 154/249

Advance MSQ

A particle moving along a straight line with uniform acceleration has velocities $7\mathrm{ms}^{-1}$ at $A$ and $17\mathrm{ms}^{-1}$ at $B$ . $C$ is the mid-point of $AB$ . Then

A

the average velocity between C and B is $15 \, ms^{-1}$

B

the ratio of time to go from $A$ to $C$ and that from $C$ to $B$ is 3:2

C

the velocity at C is $10 \, ms^{-1}$

D

the average velocity between A and C is $10 \, ms^{-1}$

Question 155: Palette 155/249

Advance MSQ

An aeroplane flies along a straight line from $A$ to $B$ with a speed $v_{0}$ and back again with the same speed $v_{0}$ . A steady wind $v$ is blowing. If $AB = l$ then

A

total time for the trip is $\frac{2v_{0}l}{v_{0}^{2}-v^{2}}$ , if wind blows along the line AB.

B

total time for the trip is $\frac{2l}{\sqrt{v_0^2 - v^2}}$ , if wind blows perpendicular to the line $AB$ .

C

total time for the trip decreases because of the presence of wind.

D

total time for the trip increases because of the presence of wind.

Question 156: Palette 156/249

Advance MSQ

Acceleration of a particle which is at rest at $x = 0$ is $\vec{a} = (4 - 2x)\hat{i}$ . Select the correct alternative(s)

A

maximum speed of particle is 4 units

B

particle further comes to rest at x = 4

C

particle oscillates about x = 2

D

all of the above

Question 157: Palette 157/249

Advance MSQ

At the instant a motor bike starts from rest in a given direction, a car overtakes the motor bike, both moving in the same direction. The speed time graphs for motor bike and car are represented by OAB and CD respectively. Then

A

at t=18 s the motor bike and car are 180 m apart.

B

at $t = 18 \, \text{s}$ the motor bike and car are $720 \, \text{m}$ apart.

C

the relative distance between motor bike and car reduces to zero at t = 27 s and both are 1080 m far from origin.

D

the relative distance between motor bike and car always remains same.

Question 158: Palette 158/249

Advance MSQ

A car is moving rectilinearly on a horizontal path with acceleration $a_{0}$ . A person sitting inside the car observes that an insect S is crawling up the screen with an acceleration a. If $\theta$ is the inclination of the screen with the horizontal, then the acceleration of the insect

A

perpendicular to screen is $a_{0} \tan \theta$

B

perpendicular to screen is $a_{0}\sin\theta$

C

along the horizontal is $a_{0}-a\cos\theta$

D

parallel to screen is $a + a_{0} \cos \theta$

Question 159: Palette 159/249

Advance MSQ

A particle having a velocity $v = v_{0}$ at t = 0 is decelerated at the rate $|a| = \alpha \sqrt{v}$ , where $\alpha$ is a positive constant.

A

The particle comes to rest at $t = \frac{2\sqrt{v_0}}{\alpha}$ .

B

The particle will come to rest at infinity.

C

The distance travelled by the particle is $\frac{2v_0^{3/2}}{\alpha}$ .

D

The distance travelled by the particle is $\frac{2}{3}\frac{v_{0}^{3/2}}{\alpha}$

Question 160: Palette 160/249

Advance MSQ

A car starts moving rectilinearly (initial velocity zero) first with an acceleration of $5 \, ms^{-2}$ then uniformly and finally decelerating at the same rate till it stops. Total time of journey is 25 s and average velocity during the journey is $72 \, kmh^{-1}$ . Then

A

total distance travelled by the car is 500 m.

B

maximum speed attained during the journey is $25 \, ms^{-1}$ .

C

car travels with uniform speed for 15 s.

D

car accelerates for 5 s and decelerates also for 5 s.

Question 161: Palette 161/249

Advance MSQ

For a moving body, which of the following statement(s) is/are true?

A

If its speed changes but direction of motion does not change, its velocity may remain constant.

B

If its speed changes, its velocity must change and it must have some acceleration.

C

If its velocity changes, its speed must change and it must have some acceleration.

D

If its velocity changes, its speed may or may not change, and it must have some acceleration.

Question 162: Palette 162/249

Advance MSQ

A body is moving along a straight line. Its distance $x_{t}$ from a point on its path at a time t after passing that point is given by $x_{t}=8t^{2}-3t^{3}$ , where $x_{t}$ is in metre and t is in second.

A

Average speed during the interval t = 0 s to t = 4 s is $20.21 \, ms^{-1}$ .

B

Average velocity during the interval t = 0 s to $t = 4 \, s$ is $-16 \, ms^{-1}$ .

C

The body starts from rest and at $t=\frac{16}{9}$ s it reverses its direction of motion at $x_{t}=8.43$ m from the start.

D

It has an acceleration of $-56 \, ms^{-2}$ at t = 4 s.

Question 163: Palette 163/249

Advance MSQ

Let $\vec{r}$ be the radius vector of a particle in motion about some reference point and $r$ its modulus. Similarly $\vec{v}$ be the velocity vector and $v$ its modulus, then

A

$|d\vec{r}|\neq dr$

B

$v\neq \frac{dr}{dt}$

C

$v = \frac{dr}{dt}$

D

$v = \left|\frac{d\vec{r}}{dt}\right|$

Question 164: Palette 164/249

Advance MSQ

Two particles $P$ and $Q$ move in a straight line $AB$ towards each other. $P$ starts from $A$ with velocity $u_{1}$ and an acceleration $a_{1}$ . $Q$ starts from $B$ with velocity $u_{2}$ and acceleration $a_{2}$ . They pass each other at the midpoint of $AB$ and arrive at the other ends of $AB$ with equal velocities.

A

They meet at midpoint at time $t = \frac{2(u_2 - u_1)}{(a_1 - a_2)}$ .

B

The length of path specified i.e. $AB$ is $l = \frac{4(u_2 - u_1)(a_1u_2 - a_2u_1)}{(a_1 - a_2)^2}$ .

C

They reach the other ends of $AB$ with equal velocities if $(u_2 + u_1)(a_1 - a_2) = 8(a_1u_2 - a_2u_1)$ .

D

They reach the other ends of $AB$ with equal velocities if $(u_2 - u_1)(a_1 + a_2) = 8(a_2u_1 - a_1u_2)$ .

Question 165: Palette 165/249

Advance MSQ

Consider a body moving rectilinearly under the influence of constant acceleration $\vec{a}$ . Let $\vec{v}$ denote the velocity of the body at any instant of time. Which of the following argument(s) is/are correct?

A

Speed must decrease when $\vec{a}$ is negative.

B

Speed must increase when $\vec{a}$ is negative for the body that starts from rest initially.

C

Speed will increase when both $\vec{v}$ and $\vec{a}$ are both negative.

D

Speed will decrease when $\vec{v}$ is negative and $\vec{a}$ positive.

Question 166: Palette 166/249

Advance MSQ

The co-ordinate of the particle in $x - y$ plane are given as $x = 2 + 2t + 4t^2$ and $y = 4t + 8t^2$ . The motion of the particle is

A

along a parabolic path

B

non-uniformly accelerated

C

along a straight line

D

uniformly accelerated

Question 167: Palette 167/249

Advance MSQ

Two particles A and B are located in x-y plane at points $(0,0)$ and $(0,4\mathrm{~m})$ . They simultaneously start moving with velocities $\vec{v}_{A}=2\hat{j}~ms^{-1}$ and $\vec{v}_{B}=2\hat{i}~ms^{-1}$ . Select the correct alternative(s)

A

the distance between them is constant

B

the distance between them first decreases and then increases

C

time after which they are at minimum distance is 1 s

D

the shortest distance between them is $2\sqrt{2}$ m

Question 168: Palette 168/249

Advance MSQ

Consider a body moving rectilinearly with velocity v under the influence of an acceleration a. Which of the following statement(s) is/are correct?

A

The direction of a must have some correlation with the direction of v.

B

a can be non-zero when v = 0

C

a must be zero when v = 0

D

a may be zero when $v \neq 0$

Question 169: Palette 169/249

Advance MSQ

For a particle moving rectilinearly, the velocity-time $(\vec{v}-t)$ graph is plotted. Which of the following argument(s) is/are correct to explain the facts about its motion?

A

The acceleration of the particle remains constant.

B

The particle changes its direction of motion at some point.

C

The initial and final speeds of the particle are the same.

D

The displacement of the particle is zero.

Question 170: Palette 170/249

Advance MSQ

Two stationary objects when seen by an observer that moves with a constant speed along the line joining them (the stationary objects) will

A

move in the same direction

B

move in opposite directions

C

have the same velocity

D

have the same speed

Question 171: Palette 171/249

Advance MSQ

A particle moving along x-axis has its velocity (v) varying with x co-ordinate (x) as $v = \sqrt{x}$ . Then

A

initial velocity of particle is zero

B

motion is uniformly accelerated

C

acceleration of particle at x = 2 m is $\frac{1}{2}$ ms $^{-2}$

D

acceleration of particle at x = 4 m is $1 \, ms^{-2}$

Question 172: Palette 172/249

Advance MSQ

Displacement time graph of a particle moving in a straight line is as shown in figure

A

in region A acceleration is positive

B

in region B acceleration is negative

C

in region $C$ motion is uniform

D

in region D acceleration is negative

Question 173: Palette 173/249

Advance MSQ

A particle moves on a straight line position at any time $t$ is given by $x = x_0 e^{-kt}$ , where $k$ is a constant. Select the correct statement(s).

A

Distance moved is infinite.

B

Distance moved during total motion is finite

C

Average speed for total motion is zero.

D

Average speed for total motion is infinite.

Question 174: Palette 174/249

Advance MSQ

The motion of the body starting from rest is governed by the relation $\frac{dv}{dt} = -v^{2} + 2v - 1$ , where v is speed in $ms^{-1}$ and t is time in second, then select the correct statement(s).

A

Terminal velocity is $1 \, ms^{-1}$ .

B

The magnitude of initial acceleration is $1 \, ms^{-2}$ .

C

Instantaneous speed is $v = -\frac{1}{1 + t}$ .

D

The speed is $1.5 \, ms^{-1}$ when acceleration is one fourth of its initial value

Question 175: Palette 175/249

Advance MSQ

In the figure is shown the position of a particle moving on the x-axis as a function of time. Then

A

the particle has come to rest for 6 times

B

the maximum speed is at t = 6 s

C

the velocity remain positive for t = 0 to t = 6 s

D

the average velocity for the total period shown is negative

Question 176: Palette 176/249

Advance MSQ

A particle moves with an initial velocity $v_{0}$ and retardation $\alpha v$ , where v is its velocity at any time t. Select the correct statement(s).

A

The particle will cover a total distance $\frac{v_{0}}{\alpha}$

B

The particle comes to rest after a time $\frac{1}{\alpha}$

C

The particle will continue to move for a very long time

D

The velocity of the particle will become $\frac{v_0}{2}$ after a time $\frac{1}{\alpha}$

Question 177: Palette 177/249

Advance MSQ

A particle starts moving rectilinearly from the origin along the x-axis. The graph between the square of speed and position of the particle is given in the figure. Select the correct statement(s).

A

Acceleration of the particle is $15 \, ms^{-1}$ at $t = \frac{1}{2} \, s$

B

Acceleration of the particle is $7.5 \, \text{ms}^{-1}$ at $t = 1 \, \text{s}$

C

Acceleration of the particle is constant

D

At t = 1 s, velocity of particle is $12.5 \, ms^{-1}$

Question 178: Palette 178/249

Advance MSQ

Mark the correct statement for a particle going on a straight line

A

If the velocity and acceleration have opposite sign, the object is slowing down.

B

If the position and velocity have opposite sign, the particle is moving towards the origin.

C

If the velocity is zero at an instant, the acceleration should also be zero at that instant.

D

If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.

Question 179: Palette 179/249

Advance MSQ

Acceleration vs time graph for a particle moving in straight line is as shown in figure. If particle starts from rest at t=0, then which of the following curve is true for the same particle

A

B

C

D

Question 180: Palette 180/249

Advance MSQ

A train accelerates from rest for time $t_{1}$ , at a constant acceleration $\alpha$ for distance x. Then it decelerates to rest at constant retardation $\beta$ in time $t_{2}$ for distance y. Then

A

$\frac{x}{y} = \frac{\beta}{\alpha}$

B

$\frac{\beta}{\alpha} = \frac{t_{1}}{t_{2}}$

C

$\frac{x}{y} = \frac{t_{1}}{t_{2}}$

D

$x = y$

Question 181: Palette 181/249

Advance MSQ

From $v - t$ graph shown in figure. can draw the following conclusion

A

between $t = 1$ is to $t = 2$ s speed of particle is decreasing

B

between $t = 2 \, \text{s}$ to $t = 3 \, \text{s}$ speed of particle is increasing

C

between t = 5 to t = 6 s acceleration of particle is negative

D

between t=0 to t=4 s particle changes, its direction of motion twice

Question 182: Palette 182/249

Advance MSQ

Which of the following statement(s) is/are incorrect?

A

Distance and speed can never be negative

B

Distance and speed may decrease or increase

C

Distance is always greater than magnitude of displacement

D

Speed is always greater than magnitude of velocity

Question 183: Palette 183/249

Advance MSQ

A car accelerates from rest at a constant rate of $2 \, ms^{-2}$ for some time. Then it retards (speed decrease) at a constant rate of $4 \, ms^{-2}$ and comes to rest. It remains in motion for a time of 6 s.

A

Its maximum speed is $8 \, ms^{-1}$

B

Its maximum speed is $6 \, ms^{-1}$

C

It travelled a total distance of 24 m

D

It travelled a total distance of 18 m

Question 184: Palette 184/249

Advance MSQ

A particle moves along a straight line and its velocity depends on time as $v = 4t - t^2$ . Then for first 5 s, the

A

Average velocity is $\frac{25}{3}$ ms $^{-1}$

B

Average speed is $10 \, ms^{-1}$

C

Average velocity is $\frac{5}{3}$ ms $^{-1}$

D

Acceleration is $4 \, ms^{-2}$ at t = 0

Question 185: Palette 185/249

Advance MCQ

Statement-1: In a uniformly accelerated motion, acceleration time graph is straight line with positive slope. Statement-2: Acceleration is rate of change of velocity.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 186: Palette 186/249

Advance MCQ

Statement-1: A body having non-zero acceleration can have a constant velocity. Statement-2: Acceleration is the rate of change of velocity.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 187: Palette 187/249

Advance MCQ

Statement-1: Irrespective of the kind of motion possessed by a body, the body will always stay at rest in a reference frame attached to the body itself. Statement-2: The relative velocity of a body with respect to itself is always zero.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 188: Palette 188/249

Advance MCQ

Statement-1: The instantaneous velocity does not depend on instantaneous position vector. Statement-2: The instantaneous velocity and average velocity of a particle are always same.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 189: Palette 189/249

Advance MCQ

Statement-1: A balloon ascends from the surface of earth with constant speed. When it was at a height 50 m above the ground, a packet is dropped from it. To an observer on the balloon, the displacement of the packet, from the moment it is dropped to the moment it reaches the surface of earth, is 50 m. Statement-2: Displacement (vector) depends upon the reference frame used to measure it.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 190: Palette 190/249

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Statement-1: A man who can swim at a speed $v$ relative to water wants to cross the river of width $d$ , flowing with speed $u$ . He cannot reach a point $P$ just opposite to him across the river, if $u > v$ . Statement-2: The time to reach the opposite point $P$ across the river is $\frac{d}{\sqrt{v^2 - u^2}}$ and if $u > v$ time will come out to be imaginary.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 191: Palette 191/249

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Statement-1: When a particle moves along a straight line magnitude of its average velocity is equal to its average speed over any time interval. Statement-2: For one dimensional motion displacement and distance may or may not be equal.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 192: Palette 192/249

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Statement-1: If two particles, moving with constant velocities are to meet, the relative velocity must be along the line joining the two particles. Statement-2: Relative velocity means motion of one particle as viewed from the other.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 193: Palette 193/249

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Statement-1: Two balls are dropped one after the other from a tall tower. The distance between them increases linearly with time (that elapses after the second ball is dropped and before the first hits ground). Statement-2: Relative acceleration is zero, whereas relative velocity non-zero in the above situation.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 194: Palette 194/249

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Statement-1: $\left|\frac{d\vec{v}}{dt}\right|=\frac{d}{dt}|\vec{v}|$ , where $\vec{v}$ has its usual meaning. Statement-2: Acceleration is the rate of change of velocity.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 195: Palette 195/249

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Statement-1: $x - t$ graph, for a particle undergoing rectilinear motion, can be as shown in the figure. Statement-2: Infinitesimal changes in velocity are physically possible only in infinitesimal time.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 196: Palette 196/249

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Statement-1: Area under velocity-time graph gives displacement. Statement-2: Area under acceleration-time graph gives average velocity.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 197: Palette 197/249

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Comprehension Passage: Comprehension - 1

Two particles A and B start from rest at the origin x=0 and move along a straight line such that $a_{A}=(6t-3)\mathrm{ms}^{-2}$ and $a_{B}=(12t^{2}-8)\mathrm{ms}^{-2}$ , where t is in seconds. Based on the above facts, answer the following questions. Total distance travelled by A at t = 4 s is

A

40 m

B

41 m

C

42 m

D

43 m

Question 198: Palette 198/249

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Comprehension Passage: Comprehension - 1

Two particles A and B start from rest at the origin x=0 and move along a straight line such that $a_{A}=(6t-3)\mathrm{ms}^{-2}$ and $a_{B}=(12t^{2}-8)\mathrm{ms}^{-2}$ , where t is in seconds. Based on the above facts, answer the following questions. Total distance travelled by B at t = 4 s is

A

192 m

B

184 m

C

196 m

D

200 m

Question 199: Palette 199/249

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Comprehension Passage: Comprehension - 1

Two particles A and B start from rest at the origin x=0 and move along a straight line such that $a_{A}=(6t-3)\mathrm{ms}^{-2}$ and $a_{B}=(12t^{2}-8)\mathrm{ms}^{-2}$ , where t is in seconds. Based on the above facts, answer the following questions. The distance between them at t = 4 s is

A

144 m

B

148 m

C

152 m

D

156 m

Question 200: Palette 200/249

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Comprehension Passage: Comprehension - 2

A particle initially at x=10 m, starts moving along the positive x-axis with an initial velocity of $40 \, ms^{-1}$ under the influence of an acceleration of $10 \, ms^{-2}$ directed along the negative x direction. Based on this information, answer the following questions. The particle reverses its direction of motion at time $t_{0}$ from the start. Then

A

$t_{0}=2\ s$

B

$t_{0}=4\ s$

C

$t_{0}=6\ s$

D

$t_{0}=8\ s$

Question 201: Palette 201/249

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Comprehension Passage: Comprehension - 2

A particle initially at x=10 m, starts moving along the positive x-axis with an initial velocity of $40 \, ms^{-1}$ under the influence of an acceleration of $10 \, ms^{-2}$ directed along the negative x direction. Based on this information, answer the following questions. The maximum x -coordinate of the particle is

A

30 m

B

60 m

C

90 m

D

120 m

Question 202: Palette 202/249

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Comprehension Passage: Comprehension - 2

A particle initially at x=10 m, starts moving along the positive x-axis with an initial velocity of $40 \, ms^{-1}$ under the influence of an acceleration of $10 \, ms^{-2}$ directed along the negative x direction. Based on this information, answer the following questions. The velocity of the particle (in $\mathrm{ms}^{-1}$ ) at the origin of the coordinate system is

A

$30\sqrt{2}$ along $+x$ direction

B

$30\sqrt{2}$ along $-x$ direction

C

$10\sqrt{7}$ along $+x$ direction

D

$10\sqrt{7}$ along $-x$ direction

Question 203: Palette 203/249

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Comprehension Passage: Comprehension - 2

A particle initially at x=10 m, starts moving along the positive x-axis with an initial velocity of $40 \, ms^{-1}$ under the influence of an acceleration of $10 \, ms^{-2}$ directed along the negative x direction. Based on this information, answer the following questions. The time at which the particle crosses the origin is

A

$(4-3\sqrt{2})$ s

B

$(4+3\sqrt{2})$ s

C

$(4-\sqrt{7})$ s

D

$(4+\sqrt{7})$ s

Question 204: Palette 204/249

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Comprehension Passage: Comprehension - 3

Starting from rest, a particle moves rectilinearly along x-axis, under the influence of acceleration a which varies with time t (in second) as $a = (2t - 4) \, \text{ms}^{-2}$ . Based on this information answer the following questions. The particle comes to rest at time equal to

A

1 s

B

2 s

C

3 s

D

4 s

Question 205: Palette 205/249

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Comprehension Passage: Comprehension - 3

Starting from rest, a particle moves rectilinearly along x-axis, under the influence of acceleration a which varies with time t (in second) as $a = (2t - 4) \, \text{ms}^{-2}$ . Based on this information answer the following questions. The maximum velocity of the particle is $v_{max}$ at time $t_{0}$ (say). Then

A

$v_{max} = 2 ms^{-1}$ , along +x axis at time $t_{0} = 2 s$

B

$v_{max} = 4 ms^{-1}$ , along -x axis at time $t_{0} = 2 s$

C

$v_{max} = 2 ms^{-1}$ , along -x axis at time $t_{0} = 4 s$

D

$v_{max} = 4 ms^{-1}$ , along +x axis at time $t_{0} = 4 s$

Question 206: Palette 206/249

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Comprehension Passage: Comprehension - 3

Starting from rest, a particle moves rectilinearly along x-axis, under the influence of acceleration a which varies with time t (in second) as $a = (2t - 4) \, \text{ms}^{-2}$ . Based on this information answer the following questions. The velocity-time graph of the particle is a

A

Straight line passing through $(0, 0)$

B

Straight line passing through $(2, 0)$

C

Parabola having origin at $(4, 2)$

D

Parabola having origin at $(2, 4)$

Question 207: Palette 207/249

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Comprehension Passage: Comprehension - 4

The motion of a body falling initially from rest in a resistive medium is described by the differential equation $$ \frac {d v}{d t} = 6 - 3 v $$ where v is the velocity of the body at any instant (in ms $^{-1}$ ). Based on the above facts, answer the following questions. The initial acceleration is of the body is

A

$6 \, ms^{-2}$

B

$3 \, ms^{-2}$

C

$2 \, ms^{-2}$

D

$18 \, ms^{-2}$

Question 208: Palette 208/249

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Comprehension Passage: Comprehension - 4

The motion of a body falling initially from rest in a resistive medium is described by the differential equation $$ \frac {d v}{d t} = 6 - 3 v $$ where v is the velocity of the body at any instant (in ms $^{-1}$ ). Based on the above facts, answer the following questions. The terminal velocity i.e., the velocity at which acceleration becomes zero is given by

A

$6 \, ms^{-1}$

B

$3 \, ms^{-1}$

C

$2 \, ms^{-1}$

D

$18 \, ms^{-1}$

Question 209: Palette 209/249

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Comprehension Passage: Comprehension - 4

The motion of a body falling initially from rest in a resistive medium is described by the differential equation $$ \frac {d v}{d t} = 6 - 3 v $$ where v is the velocity of the body at any instant (in ms $^{-1}$ ). Based on the above facts, answer the following questions. The velocity at any time $t$ is given by

A

$v = e^{-3t}$

B

$v = 1 - e^{-3t}$

C

$v = \frac{1}{2}(1 - e^{-3t})$

D

$v = 2(1 - e^{-3t})$

Question 210: Palette 210/249

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Comprehension Passage: Comprehension - 4

The motion of a body falling initially from rest in a resistive medium is described by the differential equation $$ \frac {d v}{d t} = 6 - 3 v $$ where v is the velocity of the body at any instant (in ms $^{-1}$ ). Based on the above facts, answer the following questions. The acceleration (a) of the body as the function of time is

A

$a = 2e^{-3t}$

B

$a = 3e^{-2t}$

C

$a = 6e^{-3t}$

D

$a = 6e^{-2t}$

Question 211: Palette 211/249

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Comprehension Passage: Comprehension - 5

A particle moves in the xy plane, such that at any instant t, its x and y coordinates are given by $$ x = a \sin (\omega t) $$ and $$ y = a \left[ 1 - \cos (\omega t) \right] $$ where a and $\omega$ are constants. Based on the above facts, answer the following questions. The magnitude of the velocity of the particle is

A

$a\omega$

B

$a\omega \sin (\omega t)$

C

$a\omega \cos (\omega t)$

D

$a\omega [\sin (\omega t) + \cos (\omega t)]$

Question 212: Palette 212/249

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Comprehension Passage: Comprehension - 5

A particle moves in the xy plane, such that at any instant t, its x and y coordinates are given by $$ x = a \sin (\omega t) $$ and $$ y = a \left[ 1 - \cos (\omega t) \right] $$ where a and $\omega$ are constants. Based on the above facts, answer the following questions. The equation of trajectory followed by the particle is

A

$x = \sqrt{2ay}$

B

$x = \sqrt{2ay}\sqrt{1 - \frac{y}{2a}}$

C

$x = 4ay^{2}$

D

None of these

Question 213: Palette 213/249

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Comprehension Passage: Comprehension - 5

A particle moves in the xy plane, such that at any instant t, its x and y coordinates are given by $$ x = a \sin (\omega t) $$ and $$ y = a \left[ 1 - \cos (\omega t) \right] $$ where a and $\omega$ are constants. Based on the above facts, answer the following questions. The magnitude of the acceleration of the particle is

A

$a\omega$

B

$a\omega^{2}$

C

$\frac{a\omega^{2}}{2}$

D

$\frac{a\omega^{2}}{3}$

Question 214: Palette 214/249

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Comprehension Passage: Comprehension - 6

A small ball is pushed with a speed v from A. It moves on a smooth surface and collides with the wall at B at distance d from A. During impact loses one third of its velocity. Based on the above facts, answer the following questions. The average velocity of the ball during its motion from $A$ to $B$ and back to $A$ will be

A

zero

B

$\frac{v}{2}$

C

$\frac{v}{3}$

D

$\frac{2v}{3}$

Question 215: Palette 215/249

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Comprehension Passage: Comprehension - 6

A small ball is pushed with a speed v from A. It moves on a smooth surface and collides with the wall at B at distance d from A. During impact loses one third of its velocity. Based on the above facts, answer the following questions. The total time taken by the ball in moving from A to B and back to A is T. Then T equals

A

$\frac{2d}{v}$

B

$\frac{3d}{v}$

C

$\frac{4d}{v}$

D

$\frac{5d}{2v}$

Question 216: Palette 216/249

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Comprehension Passage: Comprehension - 6

A small ball is pushed with a speed v from A. It moves on a smooth surface and collides with the wall at B at distance d from A. During impact loses one third of its velocity. Based on the above facts, answer the following questions. The average speed during the journey from $A$ to $B$ and back to $A$ is

A

$\frac{v}{5}$

B

$\frac{2v}{5}$

C

$\frac{3v}{5}$

D

$\frac{4v}{5}$

Question 217: Palette 217/249

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Comprehension Passage: Comprehension - 7

A car accelerates from rest with $2 \, ms^{-2}$ on a straight track and then it comes to rest applying its brakes. The total distance travelled by the car is 100 m in 20 s. Based on the above facts, answer the following questions. The maximum speed attained by the car is

A

$5 \, ms^{-1}$

B

$10 \, ms^{-1}$

C

$15 \, ms^{-1}$

D

$20 \, ms^{-1}$

Question 218: Palette 218/249

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Comprehension Passage: Comprehension - 7

A car accelerates from rest with $2 \, ms^{-2}$ on a straight track and then it comes to rest applying its brakes. The total distance travelled by the car is 100 m in 20 s. Based on the above facts, answer the following questions. The duration for which the brakes were applied is

A

10 s

B

5 s

C

15 s

D

16 s

Question 219: Palette 219/249

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Comprehension Passage: Comprehension - 7

A car accelerates from rest with $2 \, ms^{-2}$ on a straight track and then it comes to rest applying its brakes. The total distance travelled by the car is 100 m in 20 s. Based on the above facts, answer the following questions. The maximum retardation given to the car is

A

$2 \, ms^{-2}$

B

$\frac{2}{3} \, ms^{-2}$

C

$\frac{4}{3} \, ms^{-2}$

D

$\frac{5}{3} \, ms^{-2}$

Question 220: Palette 220/249

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Comprehension Passage: Comprehension - 7

A car accelerates from rest with $2 \, ms^{-2}$ on a straight track and then it comes to rest applying its brakes. The total distance travelled by the car is 100 m in 20 s. Based on the above facts, answer the following questions. The average speed of the car for the entire tenure of motion is

A

$5 \, ms^{-1}$

B

$6 \, ms^{-1}$

C

$8 \, ms^{-1}$

D

$8.2 \, ms^{-1}$

Question 221: Palette 221/249

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Comprehension Passage: Comprehension - 7

A car accelerates from rest with $2 \, ms^{-2}$ on a straight track and then it comes to rest applying its brakes. The total distance travelled by the car is 100 m in 20 s. Based on the above facts, answer the following questions. The distance covered during acceleration is

A

25 m

B

15 m

C

10 m

D

5 m

Question 222: Palette 222/249

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Comprehension Passage: Comprehension - 7

A car accelerates from rest with $2 \, ms^{-2}$ on a straight track and then it comes to rest applying its brakes. The total distance travelled by the car is 100 m in 20 s. Based on the above facts, answer the following questions. The distance covered during retardation is

A

85 m

B

75 m

C

50 m

D

25 m

Question 223: Palette 223/249

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Comprehension Passage: Comprehension - 8

A body falling from a height H hits an inclined plane in its path at a height $h( < H)$ . As a result of this impact, the direction of the velocity of the body becomes horizontal. Based on the above facts, answer the following questions. The value of $\frac{h}{H}$ for which the body will take the maximum time to reach the ground is

A

$\frac{1}{\sqrt{2}}$

B

$\sqrt{2}$

C

$\frac{1}{2}$

D

2

Question 224: Palette 224/249

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Comprehension Passage: Comprehension - 8

A body falling from a height H hits an inclined plane in its path at a height $h( < H)$ . As a result of this impact, the direction of the velocity of the body becomes horizontal. Based on the above facts, answer the following questions. The time taken by the body to hit the ground is

A

$T = 2\sqrt{\frac{H}{g}}$

B

$T = 4\sqrt{\frac{H}{g}}$

C

$T = \sqrt{\frac{2H}{g}}$

D

$T = \sqrt{\frac{3H}{g}}$

Question 225: Palette 225/249

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Comprehension Passage: Comprehension - 9

A body is projected from the ground vertically upwards. The body is observed to be at height h above the ground at two times $t_{1}$ and $t_{2}$ while ascending and descending respectively. Based on the above facts, answer the following questions. The height $h$ in terms of $t_1$ and $t_2$ is

A

$h = gt_1t_2$

B

$h = 2gt_1t_2$

C

$h = \frac{1}{2} gt_1t_2$

D

$h = \frac{1}{4} gt_1t_2$

Question 226: Palette 226/249

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Comprehension Passage: Comprehension - 9

A body is projected from the ground vertically upwards. The body is observed to be at height h above the ground at two times $t_{1}$ and $t_{2}$ while ascending and descending respectively. Based on the above facts, answer the following questions. The velocity of projection $(u)$ must be

A

$u = \frac{1}{2} g(t_1 + t_2)$

B

$u = \frac{1}{4} g(t_1 + t_2)$

C

$u = 2g(t_1 + t_2)$

D

$u = 4g(t_1 + t_2)$

Question 227: Palette 227/249

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Comprehension Passage: Comprehension - 9

A body is projected from the ground vertically upwards. The body is observed to be at height h above the ground at two times $t_{1}$ and $t_{2}$ while ascending and descending respectively. Based on the above facts, answer the following questions. The maximum height (H) reached by the body is

A

$H = \frac{1}{2} g t_{1}^{2}$

B

$H = \frac{1}{2} g t_{2}^{2}$

C

$H = \frac{1}{8} g(t_{1} + t_{2})^{2}$

D

$H = \frac{1}{4} g(t_{1} + t_{2})^{2}$

Question 228: Palette 228/249

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Comprehension Passage: Comprehension - 9

A body is projected from the ground vertically upwards. The body is observed to be at height h above the ground at two times $t_{1}$ and $t_{2}$ while ascending and descending respectively. Based on the above facts, answer the following questions. The velocity $(v)$ of the body at height $\frac{h}{2}$ is

A

$v = \frac{1}{4} gt_{1}$

B

$v = \frac{1}{4} gt_{2}$

C

$v = \frac{1}{2} g\sqrt{t_1^2 + t_2^2}$

D

$v = \frac{1}{4} g\sqrt{t_1t_2}$

Question 229: Palette 229/249

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Comprehension Passage: Comprehension - 9

A body is projected from the ground vertically upwards. The body is observed to be at height h above the ground at two times $t_{1}$ and $t_{2}$ while ascending and descending respectively. Based on the above facts, answer the following questions. The velocity of the particle at half the maximum height.

A

$\frac{g}{2}\sqrt{t_{1}^{2}+t_{2}^{2}}$

B

$\frac{g}{4}(t_{1}^{2}+t_{2}^{2})$

C

$\frac{g}{2\sqrt{2}}(t_{1}+t_{2})$

D

$\frac{g}{\sqrt{2}}(t_{1}+t_{2})$

Question 230: Palette 230/249

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Comprehension Passage: Comprehension - 10

If the velocity v of a particle moving along a straight line decreases linearly with its displacement s from $20 \, ms^{-1}$ to a value approaching zero at s = 30 m. Based on the above facts, answer the following questions. Acceleration of the particle at $s = 15 \mathrm{~m}$ is

A

$\frac{2}{3} \mathrm{~ms}^{-2}$

B

$-\frac{2}{3} \mathrm{~ms}^{-2}$

C

$\frac{20}{3} \mathrm{~ms}^{-2}$

D

$-\frac{20}{3} \mathrm{~ms}^{-2}$

Question 231: Palette 231/249

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Comprehension Passage: Comprehension - 10

If the velocity v of a particle moving along a straight line decreases linearly with its displacement s from $20 \, ms^{-1}$ to a value approaching zero at s = 30 m. Based on the above facts, answer the following questions. The time taken by the particle to reach the 30 m position is

A

1.5 s

B

3 s

C

6 s

D

Infinite

Question 232: Palette 232/249

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Comprehension Passage: Comprehension - 11

Buses are going from one city to other and vice-versa. The buses start at regular interval of 5 minutes each from station A to B and station B to A each with same speed $60 \, kmh^{-1}$ . The distance between two stations is 30 km. A bus marked A starts from city A and finds buses approaching from opposite direction. Based on the above facts, answer the following questions. The time interval after which bus A will meet two buses coming from opposite side is

A

5 min

B

2.5 min

C

1.25 min

D

10 min

Question 233: Palette 233/249

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Comprehension Passage: Comprehension - 11

Buses are going from one city to other and vice-versa. The buses start at regular interval of 5 minutes each from station A to B and station B to A each with same speed $60 \, kmh^{-1}$ . The distance between two stations is 30 km. A bus marked A starts from city A and finds buses approaching from opposite direction. Based on the above facts, answer the following questions. The distance travelled by bus A to meet two buses from opposite side is

A

2.5 km

B

5 km

C

10 km

D

None of these

Question 234: Palette 234/249

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Comprehension Passage: Comprehension - 11

Buses are going from one city to other and vice-versa. The buses start at regular interval of 5 minutes each from station A to B and station B to A each with same speed $60 \, kmh^{-1}$ . The distance between two stations is 30 km. A bus marked A starts from city A and finds buses approaching from opposite direction. Based on the above facts, answer the following questions. How many buses the bus A will meet on way from city A to city B?

A

6

B

5

C

12

D

11

Question 235: Palette 235/249

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Comprehension Passage: Comprehension - 12

A particle moves in positive x-direction according to law $x = 12t - t^{2}$ m. where t time in second. (Take +ve x-direction as +ve). Based on the above facts, answer the following questions. Average velocity from $t = 0$ to $t = 8 \, \mathrm{s}$ is

A

$4 \, \mathrm{ms}^{-1}$

B

$6 \, \mathrm{ms}^{-1}$

C

$8 \, \mathrm{ms}^{-1}$

D

$-4 \, \mathrm{ms}^{-1}$

Question 236: Palette 236/249

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Comprehension Passage: Comprehension - 12

A particle moves in positive x-direction according to law $x = 12t - t^{2}$ m. where t time in second. (Take +ve x-direction as +ve). Based on the above facts, answer the following questions. Average speed from t=0 to t=8 s is

A

$4 \, ms^{-1}$

B

$5 \, ms^{-1}$

C

$6 \, ms^{-1}$

D

$8 \, ms^{-1}$

Question 237: Palette 237/249

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Comprehension Passage: Comprehension - 12

A particle moves in positive x-direction according to law $x = 12t - t^{2}$ m. where t time in second. (Take +ve x-direction as +ve). Based on the above facts, answer the following questions. Average acceleration from $t = 0$ s to $t = 8$ s is

A

$-\frac{1}{4} \, \mathrm{ms}^{-2}$

B

$+\frac{1}{4} \, \mathrm{ms}^{-2}$

C

$-\frac{1}{2} \, \mathrm{ms}^{-2}$

D

$-2 \, \mathrm{ms}^{-2}$

Question 238: Palette 238/249

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Comprehension Passage: Comprehension - 13

A particle starts from rest from the origin with a time varying acceleration $a = (2t - 4)$ , where t is in seconds and a in $ms^{-2}$ . Assuming the particle to move rectilinearly. Based on the above facts, answer the following questions. Particle comes to rest (after a time) at

A

1 s

B

4 s

C

3 s

D

2 s

Question 239: Palette 239/249

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Comprehension Passage: Comprehension - 13

A particle starts from rest from the origin with a time varying acceleration $a = (2t - 4)$ , where t is in seconds and a in $ms^{-2}$ . Assuming the particle to move rectilinearly. Based on the above facts, answer the following questions. The speed of the particle moving in negative direction is maximum at time t. Then t equals

A

3 s

B

4 s

C

2 s

D

1 s

Question 240: Palette 240/249

Advance MCQ

Comprehension Passage: Comprehension - 13

A particle starts from rest from the origin with a time varying acceleration $a = (2t - 4)$ , where t is in seconds and a in $ms^{-2}$ . Assuming the particle to move rectilinearly. Based on the above facts, answer the following questions. The distance travelled by the particle from the start to the moment when it comes to rest is

A

$\frac{16}{3}$ m

B

2 m

C

3 m

D

None of these

Question 241: Palette 241/249

Advance MCQ

Comprehension Passage: Comprehension - 14

A person standing on the roof of a building throws a ball vertically upward at an instant t=0. The ball leaves his hand with an upward speed $20 \, ms^{-1}$ and it is then in free fall. The ball rises to a certain height and then moves down. On its way down, the ball just misses to hit the roof of the building and keeps falling towards the earth. The ball hits earth at t = 5 s. Considering that

(i) the vertically upward direction is the positive $y$ -direction

(ii) the position of ball at t = 0 is the origin

(iii) the ball does not rebound and comes to rest at the same place where it hits earth and

(iv) air resistance is negligible, answer these questions. $\left(\text{Take } g = 10 \text{ ms}^{-2}\right)$

Based on the above facts, answer the following questions.

Position-time graph for the given motion of the ball is

A

B

C

D

Question 242: Palette 242/249

Advance MCQ

Comprehension Passage: Comprehension - 14

A person standing on the roof of a building throws a ball vertically upward at an instant t=0. The ball leaves his hand with an upward speed $20 \, ms^{-1}$ and it is then in free fall. The ball rises to a certain height and then moves down. On its way down, the ball just misses to hit the roof of the building and keeps falling towards the earth. The ball hits earth at t = 5 s. Considering that

(i) the vertically upward direction is the positive $y$ -direction

(ii) the position of ball at t = 0 is the origin

(iii) the ball does not rebound and comes to rest at the same place where it hits earth and

(iv) air resistance is negligible, answer these questions. $\left(\text{Take } g = 10 \text{ ms}^{-2}\right)$

Based on the above facts, answer the following questions.

Velocity of the ball will vary with time as

A

B

C

D

Question 243: Palette 243/249

Advance MCQ

Comprehension Passage: Comprehension - 14

A person standing on the roof of a building throws a ball vertically upward at an instant t=0. The ball leaves his hand with an upward speed $20 \, ms^{-1}$ and it is then in free fall. The ball rises to a certain height and then moves down. On its way down, the ball just misses to hit the roof of the building and keeps falling towards the earth. The ball hits earth at t = 5 s. Considering that

(i) the vertically upward direction is the positive $y$ -direction

(ii) the position of ball at t = 0 is the origin

(iii) the ball does not rebound and comes to rest at the same place where it hits earth and

(iv) air resistance is negligible, answer these questions. $\left(\text{Take } g = 10 \text{ ms}^{-2}\right)$

Based on the above facts, answer the following questions.

Acceleration of the ball will vary with time as

A

B

C

D

Question 244: Palette 244/249

Advance MCQ

Comprehension Passage: Comprehension - 15

The position of a particle is moving along the x-axis depends on the time according to the equation $x = 6t^{2} - t^{3}$ , where x is in metre and t in seconds. Based on the above facts, answer the following questions. Time at which velocity of the particle is maximum along positive direction of $x$ -axis is

A

1 s

B

2 s

C

3 s

D

4 s

Question 245: Palette 245/249

Advance MCQ

Comprehension Passage: Comprehension - 15

The position of a particle is moving along the x-axis depends on the time according to the equation $x = 6t^{2} - t^{3}$ , where x is in metre and t in seconds. Based on the above facts, answer the following questions. Distance travelled by the particle during time interval $t = 3 \mathrm{~s}$ to $t = 5 \mathrm{~s}$ is

A

$2 \mathrm{~m}$

B

$5 \mathrm{~m}$

C

$12 \mathrm{~m}$

D

$10 \mathrm{~m}$

Question 246: Palette 246/249

Advance MCQ

Comprehension Passage: Comprehension - 15

The position of a particle is moving along the x-axis depends on the time according to the equation $x = 6t^{2} - t^{3}$ , where x is in metre and t in seconds. Based on the above facts, answer the following questions. Average speed of the particle during time interval $t = 0$ s to $t = 6$ s is

A

$2 \, \text{ms}^{-1}$

B

Zero

C

$4 \, \text{ms}^{-1}$

D

None of these

Question 247: Palette 247/249

Advance MCQ

Comprehension Passage: Comprehension - 16

A particle is moving along x-axis and its initial velocity is $27 \, ms^{-1}$ . The acceleration of particle is given by the relation $a = (-6t) \, \text{ms}^{-2}$ , where t is in seconds. At t = 0 particle is at x = 0. Based on the above facts, answer the following questions. The velocity of particle, when it travels 26 m is

A

$21 \, ms^{-1}$

B

$15 \, ms^{-1}$

C

$24 \, ms^{-1}$

D

$18 \, ms^{-1}$

Question 248: Palette 248/249

Advance MCQ

Comprehension Passage: Comprehension - 16

A particle is moving along x-axis and its initial velocity is $27 \, ms^{-1}$ . The acceleration of particle is given by the relation $a = (-6t) \, \text{ms}^{-2}$ , where t is in seconds. At t = 0 particle is at x = 0. Based on the above facts, answer the following questions. Maximum value of velocity along positive x-direction is

A

$35 \, ms^{-1}$

B

$33 \, ms^{-1}$

C

$27 \, ms^{-1}$

D

$30 \, ms^{-1}$

Question 249: Palette 249/249

Advance MCQ

Comprehension Passage: Comprehension - 16

A particle is moving along x-axis and its initial velocity is $27 \, ms^{-1}$ . The acceleration of particle is given by the relation $a = (-6t) \, \text{ms}^{-2}$ , where t is in seconds. At t = 0 particle is at x = 0. Based on the above facts, answer the following questions. Maximum value of displacement along positive x-direction is

A

54 m

B

27 m

C

120 m

D

None of these