Question 1: Palette 1/238

Errorless NEET 2024 MCQ

The velocity (v) - time (t) plot of the motion of a body is shown below The acceleration (a) - time (t) graph that best suits this motion is

A

B

C

D

Question 2: Palette 2/238

Errorless JEE (Main) 2023 MCQ

The velocity time graph of a body moving in a straight line is shown in figure The ratio of displacement to distance travelled by the body in time 0 to 10 s is

A

1:1

B

1:4

C

1:2

D

1:3

Question 3: Palette 3/238

Errorless JEE (Main) 2023 MCQ

A car travels a distance of 'x' with speed $v_{1}$ and then same distance 'x' with speed $v_{2}$ in the same direction. The average speed of the car is

A

$\frac{v_{1}v_{2}}{2(v_{1}+v_{2})}$

B

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

C

$\frac{2x}{v_{1}+v_{2}}$

D

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

Question 4: Palette 4/238

Errorless JEE (Main) 2023 MCQ

The distance travelled by a particle is related to time t as $x = 4t^{2}$ . The velocity of the particle at t = 5s is

A

$40ms^{-1}$

B

$25ms^{-1}$

C

$20ms^{-1}$

D

$8ms^{-1}$

Question 5: Palette 5/238

Errorless JEE (Main) 2023 MCQ

A vehicle travels 4 km with speed of 3 km/h and another 4 km with speed of 5 km/h, then its average speed is

A

4.25 km/h

B

3.50 km/h

C

4.00 km/h

D

3.75 km/h

Question 6: Palette 6/238

Errorless JEE (Main) 2023 MCQ

A child stands on the edge of the cliff 10m above the ground and throws a stone horizontally with an initial speed of $5ms^{-1}$ . Neglecting the air resistance, the speed with which the stone hits the ground will be ____ $ms^{-1}$ (given, $g = 10ms^{-2}$ )

A

20

B

15

C

30

D

25

Question 7: Palette 7/238

Errorless NEET 2023 MCQ

A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is

A

$\frac{2v}{3}$

B

$\frac{4v}{3}$

C

$\frac{3v}{4}$

D

$\frac{v}{3}$

Question 8: Palette 8/238

Errorless JEE (Main) 2022 MCQ

An object of mass 5kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to [Use $g = 10 ms^{-2}$ ]

A

1:1

B

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

C

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

D

2:3

Question 9: Palette 9/238

Errorless JEE (Main) 2022 MCQ

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero

A

Momentum

B

Potential energy

C

Acceleration

D

Force

Question 10: Palette 10/238

Errorless JEE (Main) 2022 MCQ

Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_{P}(t) = \alpha t + \beta t^{2}$ and $X_{Q}(t) = ft - t^{2}$ . At what time, both the buses have same velocity

A

$\frac{\alpha - f}{1 + \beta}$

B

$\frac{\alpha + f}{2(\beta - 1)}$

C

$\frac{\alpha + f}{2(1 + \beta)}$

D

$\frac{f - \alpha}{2(1 + \beta)}$

Question 11: Palette 11/238

Errorless JEE (Main) 2022 MCQ

At time t=0 a particle starts travelling from a height $7\hat{z}$ cm in a plane keeping z coordinate constant. At any instant of time it's position along the $\hat{x}$ and $\hat{y}$ directions are defined as 3t and $5t^{3}$ respectively. At t=1s acceleration of the particle will be

A

$-30\hat{y}$

B

$30\hat{y}$

C

$3\hat{x} + 15\hat{y}$

D

$3\hat{x} + 15\hat{y} + 7\hat{z}$

Question 12: Palette 12/238

Errorless JEE (Main) 2022 MCQ

A NCC parade is going at a uniform speed of 9 km/h under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is (Given $g = 9.8 \, m/s^{2}$ )

A

5 m

B

10 m

C

19.8 m

D

24.5 m

Question 13: Palette 13/238

Errorless JEE (Main) 2022 MCQ

A ball is released from a height h. If $t_{1}$ and $t_{2}$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_{1}$ and $t_{2}$

A

$t_{1} = (\sqrt{2})t_{2}$

B

$t_{1} = (\sqrt{2} - 1)t_{2}$

C

$t_{2} = (\sqrt{2} + 1)t_{1}$

D

$t_{2} = (\sqrt{2} - 1)t_{1}$

Question 14: Palette 14/238

Errorless NEET 2022 MCQ

The ratio of the distances travelled by a freely falling body in the $1^{\mathrm{st}}$ , $2^{\mathrm{nd}}$ , $3^{\mathrm{rd}}$ , and $4^{\mathrm{th}}$ second

A

$1:3:5:7$

B

$1:1:1:1$

C

$1:2:3:4$

D

$1:4:9:16$

Question 15: Palette 15/238

Errorless NEET 2022 MCQ

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the x-axis as shown in the figure. The ratio of their respective velocity is

A

$1:2$

B

$1:\sqrt{3}$

C

$\sqrt{3}:1$

D

$1:1$

Question 16: Palette 16/238

Errorless JEE (Main) 2021 MCQ

A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is

A

35 m

B

45 m

C

50 m

D

25 m

Question 17: Palette 17/238

Errorless JEE (Main) 2021 MCQ

A scooter accelerates from rest for time $t_1$ at constant rate $a_1$ and then retards at constant rate $a_2$ for time $t_2$ and comes to rest. The correct value of $\frac{t_1}{t_2}$ will be

A

$\frac{a_1 + a_2}{a_2}$

B

$\frac{a_2}{a_1}$

C

$\frac{a_1}{a_2}$

D

$\frac{a_1 + a_2}{a_1}$

Question 18: Palette 18/238

Errorless JEE (Main) 2021 MCQ

A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is $t$ seconds, the total distance travelled is

A

$\frac{4\alpha\beta}{(\alpha+\beta)} t^2$

B

$\frac{2\alpha\beta}{(\alpha+\beta)} t^2$

C

$\frac{\alpha\beta}{2(\alpha+\beta)} t^2$

D

$\frac{\alpha\beta}{4(\alpha+\beta)} t^2$

Question 19: Palette 19/238

Errorless JEE (Main) 2021 MCQ

A rubber ball is released from a height of 5m above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball (Take $g = 10 ms^{-2}$ )

A

$3.0 ms^{-1}$

B

$3.50 ms^{-1}$

C

$2.0 ms^{-1}$

D

$2.50 ms^{-1}$

Question 20: Palette 20/238

Errorless JEE (Main) 2021 MCQ

The instantaneous velocity of a particle moving in a straight line is given as $v = \alpha t + \beta t^2$ , where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between 1s and 2s is

A

$3\alpha + 7\beta$

B

$\frac{3}{2}\alpha + \frac{7}{3}\beta$

C

$\frac{\alpha}{2} + \frac{\beta}{3}$

D

$\frac{3}{2}\alpha + \frac{7}{2}\beta$

Question 21: Palette 21/238

Errorless JEE (Main) 2021 MCQ

A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around (takes the value of g as $10m/s^{2}$ )

A

300 m

B

200 m

C

125 m

D

250 m

Question 22: Palette 22/238

Errorless JEE (Main) 2021 MCQ

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{th}$ second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap (Take $g = 9.8 \, m/s^{2}$ )

A

3 drops / 2 seconds

B

2 drops / second

C

1 drop / second

D

1 drop / 7 seconds

Question 23: Palette 23/238

Errorless JEE (Main) 2021 MCQ

A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a

A

Hyperbola

B

Straight line vertically down the plane

C

Parabola in a direction opposite to the motion of plane

D

Parabola in the direction of motion of plane

Question 24: Palette 24/238

Errorless JEE (Main) 2021 MCQ

Water drops are falling from a nozzle of a shower onto the floor from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor

A

2.94 m

B

4.18 m

C

2.45 m

D

7.35 m

Question 25: Palette 25/238

Errorless JEE (Main) 2021 MCQ

A huge circular arc of length 4.4 ly subtends an angle 4s at the centre of circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second (Given: $1ly = 9.46 \times 10^{15} m$ , $1AU = 1.5 \times 10^{11} m$ )

A

$4.1 \times 10^{8} s$

B

$4.5 \times 10^{10} s$

C

$7.2 \times 10^{8} s$

D

$3.5 \times 10^{6} s$

Question 26: Palette 26/238

Errorless JEE (Main) 2021 MCQ

The velocity-displacement graph of a particle is shown in the figure The acceleration-displacement graph of the same particle is represented by

A

B

C

D

Question 27: Palette 27/238

Errorless JEE (Main) 2021 MCQ

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by

A

B

C

D

Question 28: Palette 28/238

Errorless JEE (Main) 2021 MCQ

The velocity-displacement graph describing the motion of a bicycle is shown in the figure The acceleration-displacement graph of the bicycle's motion is best described by

A

B

C

D

Question 29: Palette 29/238

Errorless JEE (Main) 2020 MCQ

Train A and train B are running on parallel tracks in the opposite directions with speed of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/hour. Speed (in ms $^{-1}$ ) of this person as observed from train B will be close to (take the distance between the tracks as negligible)

A

30.5 ms $^{-1}$

B

29.5 ms $^{-1}$

C

31.5 ms $^{-1}$

D

28.5 ms $^{-1}$

Question 30: Palette 30/238

Errorless JEE (Main) 2020 MCQ

Starting from the origin at time t=0, with initial velocity $5\hat{j}ms^{-1}$ , a particle moves in the x-y plane with a constant acceleration of $(10\hat{i}+4\hat{j})ms^{-2}$ . At time t, its coordinates are $(20\ m,\ y_{0}m)$ . The values of t and $y_{0}$ , are respectively

A

4s and 52 m

B

2s and 24 m

C

2s and 18 m

D

5s and 25 m

Question 31: Palette 31/238

Errorless JEE (Main) 2020 MCQ

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is a height h. The time taken by the packet to reach the ground is close to [g is the acceleration due to gravity]

A

$t = \sqrt{\frac{2h}{3g}}$

B

$t = 1.8\sqrt{\frac{h}{g}}$

C

$t = 3.4\sqrt{\left(\frac{h}{g}\right)}$

D

$t = \frac{2}{3}\sqrt{\left(\frac{h}{g}\right)}$

Question 32: Palette 32/238

Errorless JEE (Main) 2020 MCQ

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6s is

A

12 m v(m/s)

B

$\frac{49}{4}m$ ↑

C

11 m

D

$\frac{37}{3}m$

Question 33: Palette 33/238

Errorless JEE (Main) 2020 MCQ

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle $60^{\circ}$ from the horizontal. On further increasing the speed of the car $(1 + \beta)v$ , this angle changes to $45^{\circ}$ . The value of $\beta$ is close to

A

0.41

B

0.50

C

0.37

D

0.73

Question 34: Palette 34/238

Errorless NEET 2020 MCQ

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is $(g=10m/s^{2})$

A

300 m

B

360 m

C

340 m

D

320 m

Question 35: Palette 35/238

Errorless JEE (Main) 2020 MCQ

A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

A

B

C

D

Question 36: Palette 36/238

Errorless JEE (Main) 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

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

C

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

D

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

Question 37: Palette 37/238

Errorless JEE (Main) 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 at time $t = 5s$

A

$6m$

B

$9m$

C

$3m$

D

$10m$

Question 38: Palette 38/238

Errorless JEE (Main) 2019 MCQ

Two particles A, B are moving on two concentric circles of radii $R_{1}$ and $R_{2}$ with equal angular speed $\omega$ . At t=0, their positions and direction of motion are shown in the figure The relative velocity $\vec{v}_{A}-\vec{v}_{B}$ at $t=\frac{\pi}{2\omega}$ is given by

A

$-\omega(R_{1}+R_{2})\hat{i}$

B

$\omega (R_1 + R_2)\hat{i}$

C

$\omega(R_{1}-R_{2})\hat{i}$

D

$\omega (R_2 - R_1)\hat{i}$

Question 39: Palette 39/238

Errorless JEE (Main) 2019 MCQ

The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight

A

$60^{0}$

B

$150^{0}$

C

$90^{0}$

D

$120^{0}$

Question 40: Palette 40/238

Errorless JEE (Main) 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

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

C

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

D

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

Question 41: Palette 41/238

Errorless JEE (Main) 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

40

B

100

C

25

D

50

Question 42: Palette 42/238

Errorless JEE (Main) 2019 MCQ

A ball is thrown upward with an initial velocity $V_{0}$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma v^{2}$ (where m is mass of the ball, v is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is

A

$\frac{1}{\sqrt{\gamma g}}\sin^{-1}\left(\sqrt{\frac{\gamma}{g}}v_{0}\right)$

B

$\frac{1}{\sqrt{\gamma g}}\tan^{-1}\left(\sqrt{\frac{\gamma}{g}}v_{0}\right)$

C

$\frac{1}{\sqrt{2\gamma g}}\tan^{-1}\left(\sqrt{\frac{2\gamma}{g}}v_{0}\right)$

D

$\frac{1}{\sqrt{\gamma g}}\ln\left(1+\sqrt{\frac{\gamma}{g}}v_{0}\right)$

Question 43: Palette 43/238

Errorless JEE (Main) 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

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

B

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

C

$b^{2}\tau$

D

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

Question 44: Palette 44/238

Errorless NEET 2019 MCQ

The speed of a swimmer in still water is 20m/s. The speed of river water is 10m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by

A

30° west

B

0°

C

60° west

D

45° west

Question 45: Palette 45/238

Errorless JEE (Main) 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)
(A)

(B)

(C)

(D)

A

(A), (B), (C)

B

(A)

C

(A), (B), (D)

D

(B), (C)

Question 46: Palette 46/238

Errorless NEET 2017; JEE (Main) 2021 MCQ

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_{1}$ . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_{2}$ . The time taken by her to walk up on the moving escalator will be

A

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

B

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

C

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

D

$t_{1} - t_{2}$

Question 47: Palette 47/238

Errorless NEET (Phase-I) 2016 MCQ

If the velocity of a particle is $v = At + Bt^{2}$ , where A and B are constants, then the distance travelled by it between 1s and 2s is

A

$\frac{3}{2}A + 4B$

B

$3A + 7B$

C

$\frac{3}{2}A + \frac{7}{3}B$

D

$\frac{A}{2} + \frac{B}{3}$

Question 48: Palette 48/238

Errorless AIPMT (Cancelled) 2015 MCQ

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x) = bx^{-2n}$ Where b and n are constants and x is the position of the particle. The acceleration of the particles as function of x, is given by

A

$-2nb^{2}x^{-4n-1}$

B

$-2b^{2}x^{-2n+1}$

C

$-2nb^{2}e^{-4n+1}$

D

$-2nb^{2}x^{-2n-1}$

Question 49: Palette 49/238

Errorless KCET 2015 MCQ

The velocity-time graph for two bodies A and B are shown. Then the acceleration of A and B are in the ratio

A

$\tan 25^{\circ}$ to $\tan 50^{\circ}$

B

$\cos 25^{\circ}$ to $\cos 50^{\circ}$

C

$\tan 25^{\circ}$ to $\tan 40^{\circ}$

D

$\sin 25^{\circ}$ to $\sin 50^{\circ}$

Question 50: Palette 50/238

Errorless WB-JEE 2015 MCQ

Particle A moves along X-axis with a uniform velocity of magnitude 10 m/s. Particle B moves with uniform velocity 20 m/s along a direction making an angle of $60^{\circ}$ with the positive direction of X-axis as shown in figure. the relative velocity of B with respect to that of A is

A

10 m/s along X-axis

B

$10\sqrt{3}$ m/s along Y-axis (perpendicular to X-axis)

C

$10\sqrt{5}$ along the bisection of the velocity of A and B

D

30 m/s along negative X-axis

Question 51: Palette 51/238

Errorless AIPMT (Cancelled) 2015 MCQ

A ship A is moving Westwards with a speed of $10kmh^{-1}$ and a ship B 100km South of A, is moving Northwards with a speed of $10kmh^{-1}$ . The time after which the distance between them becomes shortest, is

A

5h

B

$5\sqrt{2}h$

C

$10\sqrt{2}h$

D

0h

Question 52: Palette 52/238

Errorless KCET 2015 MCQ

A stone of mass 0.05 kg is thrown vertically upwards. What is the direction and magnitude of net force on the stone during its upward motion

A

0.49 N vertically downwards

B

9.8 N vertically downwards

C

0.49 N vertically upwards

D

0.98 N vertically downwards

Question 53: Palette 53/238

Errorless WB-JEE 2015 MCQ

Two particles A and B having different masses are projected from a tower with same speed. A is projected vertically upward and B vertically downward. On reaching the ground

A

Velocity of A is greater than that of B

B

Velocity of B is greater than that of A

C

Both A and B attain the same velocity

D

The particle with the larger mass attains higher velocity

Question 54: Palette 54/238

Errorless JEE (Main) 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 a n times that taken by it to reach the highest point of its path. The relation between H, u and n is

A

$2gH = n^{2}u^{2}$

B

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

C

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

D

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

Question 55: Palette 55/238

Errorless NEET 2013 MCQ

A stone falls freely under gravity. It covers distances $h_1, h_2$ and $h_3$ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between $h_1, h_2$ and $h_3$ is

A

$h_1 = h_2 = h_3$

B

$h_1 = 2h_2 = 3h_3$

C

$h_1 = \frac{h_2}{3} = \frac{h_3}{5}$

D

$h_2 = 3h_1$ and $h_3 = 3h_2$

Question 56: Palette 56/238

Errorless J & K CET 2012 MCQ

If a particle moves with an acceleration, then which of the following can remain constant

A

Both speed and velocity

B

Neither speed nor velocity

C

Only the velocity

D

Only the speed

Question 57: Palette 57/238

Errorless KCET 2012 MCQ

A person throws balls into air vertically upward in regular intervals of time of one second. The next ball is thrown when the velocity of the ball thrown earlier becomes zero. The height to which the balls rise is ... (Assume, $g = 10ms^{-2}$ )

A

$5m$

B

$10m$

C

$7.5m$

D

$20m$

Question 58: Palette 58/238

Errorless Odisha JEE 2012 MCQ

A body moves in a plane so that the displacements along the x and y axes are given by $x = 3t^{3}$ and $y = 4t^{3}$ . The velocity of the body is

A

9t

B

15t

C

$15t^{2}$

D

$25t^{2}$

Question 59: Palette 59/238

Errorless CBSE PMT (Pre.) 2012 MCQ

The motion of a particle along a straight line is described by equation :$x = 8 + 1 2 t - t ^ {3}$ where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero, is

A

$24ms^{-2}$

B

Zero

C

$6ms^{-2}$

D

$12ms^{-2}$

Question 60: Palette 60/238

Errorless Kerala PET 2012 MCQ

A ball is hung by a string from the ceiling of a car moving on a straight and smooth road. If the string is inclined towards the front side of the car making a small constant angle with the vertical, then the car is moving with

A

Constant velocity

B

Constant acceleration

C

Constant retardation

D

Increasing acceleration

E

Decreasing retardation

Question 61: Palette 61/238

Errorless AMU (Engg.) 2012 MCQ

Two trains A and B each of length 400 m are moving on two parallel tracks in the same direction (with A ahead of B) with same speed 72 km/h. The driver of B decides to overtake A and accelerates by $1 \, m/s^{2}$ . If after 50 s, B just brushes past A, calculate the original distance between A and B

A

750 m

B

1000 m

C

1250 m

D

2250 m

Question 62: Palette 62/238

Errorless AMU (Med.) 2012 MCQ

Let $\vec{r}_{1}(t)=3\hat{t}+\hat{t}t^{2}\hat{j}$ and $\vec{r}_{2}(t)=4t^{2}\hat{i}+3\hat{t}j$ represent the positions of particles 1 and 2, respectively as function of time t; $\vec{r}_{1}(t)$ and $\vec{r}_{2}(t)$ are in meter and t in second. The relative speed of the two particles at the instant t=1s, will be

A

1m/s

B

$3\sqrt{2}$ m/s

C

$5\sqrt{2}$ m/s

D

$7\sqrt{2}$ m/s

Question 63: Palette 63/238

Errorless AMU (Engg.) 2012 MCQ

A particle is projected up with an initial velocity of 80ft/sec. The ball will be at a height of 96ft from the ground after

A

2.0 and 3.0 sec

B

Only at 3.0 sec

C

Only at 2.0 sec

D

After 1 and 2 sec

Question 64: Palette 64/238

Errorless MP PET 2012 MCQ

A train accelerates from rest at a constant rate $\alpha$ for distance $x_{1}$ and time $t_1$ . After that it retards to rest at constant rate $\beta$ for distance $x_{2}$ and time $t_2$ . Which of the following relations is correct

A

$\frac{x_1}{x_2} = \frac{\alpha}{\beta} = \frac{t_1}{t_2}$

B

$\frac{x_1}{x_2} = \frac{\beta}{\alpha} = \frac{t_1}{t_2}$

C

$\frac{x_1}{x_2} = \frac{\alpha}{\beta} = \frac{t_2}{t_1}$

D

$\frac{x_1}{x_2} = \frac{\beta}{\alpha} = \frac{t_2}{t_1}$

Question 65: Palette 65/238

Errorless AMU (Engg.) 2012 MCQ

Given below are four curves describing variation of velocity with time of a particle. Which one of these describe the motion of a particle initially in positive direction with constant negative acceleration (W) (X) (Y) (Z)

A

(W)

B

(X)

C

(Y)

D

(Z)

Question 66: Palette 66/238

Errorless Kerala PMT 2012 MCQ

The graph between displacement and time for a particle moving with uniform acceleration is a

A

Straight line with a positive slope

B

Parabola

C

Ellipse

D

Straight line parallel to time axis

E

Straight line perpendicular to time axis

Question 67: Palette 67/238

Errorless Odisha JEE 2011 MCQ

The displacement of a body along $x$ -axis depends on time as $\sqrt{x} = t + 1$ . Then the velocity of body

A

Increases with time

B

Decreases with time

C

Independent of time

D

None of these

Question 68: Palette 68/238

Errorless Kerala PET 2011; AMU (Med.) 2012 MCQ

A bus begins to move with an acceleration of $1ms^{-2}$ . A man who is 48m behind the bus starts running at $10ms^{-1}$ to catch the bus. The man will be able to catch the bus after

A

6s

B

5s

C

3s

D

7s

E

8s

Question 69: Palette 69/238

Errorless Odisha JEE 2011 MCQ

A body moves with initial velocity $10ms^{-1}$ . If it covers a distance of 20m in 2s, then acceleration of the body is

A

Zero

B

$10ms^{-2}$

C

$5ms^{-2}$

D

$2ms^{-2}$

Question 70: Palette 70/238

Errorless AIEEE 2011 MCQ

An object moving with a speed of 6.25 m/s, is decelerated at a rate given by $\frac{d\nu}{dt} = -2.5\sqrt{\nu}$ where $\nu$ is the instantaneous speed. The time taken by the object, to come to rest, would be

A

1s

B

2s

C

4s

D

8s

Question 71: Palette 71/238

Errorless Kerala PMT 2011 MCQ

A stone falls freely from rest from a height h and it travels a distance $\frac{9h}{25}$ in the last second. The value of h is

A

145 m

B

100 m

C

122.5 m

D

200 m

E

175 m

Question 72: Palette 72/238

Errorless CBSE PMT (Pre.) 2011 MCQ

A boy standing at the top of a tower of 20m height drops a stone. Assuming $g = 10 \, ms^{-2}$ , the velocity with which it hits the ground is

A

5.0 m/s

B

10.0 m/s

C

20.0 m/s

D

40.0 m/s

Question 73: Palette 73/238

Errorless Kerala PET 2011 MCQ

An aircraft is flying at a height of 3400m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10s apart is $30^{\circ}$ , then the speed of the aircraft is

A

$19.63ms^{-1}$

B

$1963ms^{-1}$

C

$108ms^{-1}$

D

$196.3ms^{-1}$

E

$10.8ms^{-1}$

Question 74: Palette 74/238

Errorless Kerala PMT 2010, 11 MCQ

A graph is drawn between velocity and time for the motion of a particle. The area under the curve between the time intervals $t_1$ and $t_2$ gives

A

Momentum of the particle

B

Displacement of the particle

C

Acceleration of the particle

D

Change in velocity of the particle

E

Force on the particle

Question 75: Palette 75/238

Errorless AMU (Med.) 2010 MCQ

Select the incorrect statements from the following S1 : Average velocity is path length divided by time interval S2 : In general, speed is greater than the magnitude of the velocity S3 : A particle moving in a given direction with a non-zero velocity can have zero speed S4 : The magnitude of average velocity is the average speed

A

S2 and S3

B

S1 and S4

C

S1, S3 and S4

D

All four statements

Question 76: Palette 76/238

Errorless AMU (Engg.) 2010 MCQ

The position of a particle x (in meters) at a time t seconds is given by the relation $\vec{r} = (3t\hat{i} - t^{2}\hat{j} + 4\hat{k})$ . Calculate the magnitude of velocity of the particle after 5 seconds

A

3.55

B

5.03

C

8.75

D

10.44

Question 77: Palette 77/238

Errorless CBSE PMT 2010; Pb. PMT 2011 MCQ

A particle moves a distance x in time t according to equation $x = (t + 5)^{-1}$ . The acceleration of particle is proportional to

A

(velocity) $^{2/3}$

B

(velocity) $^{3/2}$

C

(distance) $^{2}$

D

(distance) $^{-2}$

Question 78: Palette 78/238

Errorless KCET 2010 MCQ

A train is moving slowly on a straight track with a constant speed of $2 \, ms^{-1}$ . A passenger in that train starts walking at a steady speed of $2 \, ms^{-1}$ to the back of the train in the opposite direction of the motion of the train. So to an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be

A

$4 \, ms^{-1}$

B

$2 \, ms^{-1}$

C

$2 \, ms^{-1}$ in the opposite direction of the train

D

Zero

Question 79: Palette 79/238

Errorless KCET 2010 MCQ

A motorboat covers a given distance in 6 hours moving downstream on a river. It covers the same distance in 10 hours moving upstream. The time it takes to cover the same distance in still water is

A

9 hours

B

7.5 hours

C

6.5 hours

D

8 hours

Question 80: Palette 80/238

Errorless MP PMT 2010 MCQ

A ball is thrown up under gravity $(g = 10m/sec^{2})$ . Find its velocity after 1.0 sec at a height of 10m

A

$5 m/sec^{2}$

B

5 m/sec

C

10 m/sec

D

15 m/sec

Question 81: Palette 81/238

Errorless CBSE PMT 2010 MCQ

A ball is dropped from a high rise platform at t=0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t=18s. What is the value of v (take g=10 m/s $^{2}$ )

A

60 m/s

B

75 m/s

C

55 m/s

D

40 m/s

Question 82: Palette 82/238

Errorless AMU (Med.) 2010 MCQ

A body $A$ is thrown up vertically from the ground with a velocity $V_{0}$ and another body $B$ is simultaneously dropped from a height $H$ . They meet at a height $\frac{H}{2}$ if $V_{0}$ is equal to

A

$\sqrt{2gH}$

B

$\sqrt{gH}$

C

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

D

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

Question 83: Palette 83/238

Errorless Kerala PET 2010 MCQ

Free fall of an object (in vacuum) is a case of motion with

A

Uniform velocity

B

Uniform acceleration

C

Variable acceleration

D

Constant momentum

E

Uniform speed

Question 84: Palette 84/238

Errorless DUMET 2010 MCQ

At t=0, a stone of mass 10 gm is thrown straight up from the ground level with a speed 10 m/s. After 1 s, a second stone of the same mass is thrown from the same position with a speed 20 m/s. What is the position of the first stone from the ground level at that moment (Take g=10m/s $^{2}$ )

A

10 m

B

1 m

C

2 m

D

5 m

Question 85: Palette 85/238

Errorless DUMET 2010 MCQ

Two stones of equal masses are dropped from a rooftop of height h one after another. Their separation distance against time will

A

Remain the same

B

Increase

C

Decrease

D

Be zero

Question 86: Palette 86/238

Errorless Odisha JEE 2010 MCQ

Two identical metal spheres are released from the top of a tower after t seconds of each other such that they fall along the same vertical line. If air resistance is neglected, then at any instant of time during their fall,

A

The difference in their displacements remain the same

B

The difference between their speeds remains the same

C

The difference between their heights above ground is proportional to $t^{2}$

D

The difference between their displacements is proportional to t

Question 87: Palette 87/238

Errorless Kerala PET 2010, 11; JEE (Main) 2021 MCQ

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is

A

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

B

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

C

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

D

$\sqrt{\frac{v^{2}-u^{2}}{2}}$

Question 88: Palette 88/238

Errorless AMU (Med.) 2010 MCQ

Which of the following graphs can not possibly represent one dimensional motion of a particle
(I)

(II)

(III)

(IV)

A

I and II

B

II and III

C

II and IV

D

All four

Question 89: Palette 89/238

Errorless Odisha JEE 2010 MCQ

The velocity-time and acceleration-time graphs of a particle are given as Its position-time graph may be given as

A

B

C

D

Question 90: Palette 90/238

Errorless AIIMS 2010 MCQ

Assertion: The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval. Reason: Velocity is a vector quantity and speed is a scalar quantity.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 91: Palette 91/238

Errorless AIIMS 2010 MCQ

A balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is

A

$4\sqrt{\frac{h}{g}}$

B

$2\sqrt{\frac{h}{g}}$

C

$\sqrt{\frac{2h}{g}}$

D

$\sqrt{\frac{g}{h}}$

Question 92: Palette 92/238

Errorless Kerala PET 2010 MCQ

An aeroplane flies around a square field ABCD of each side 1000 km. Its speed along AB is 250 km h $^{-1}$ , along BC 500 km h $^{-1}$ , along CD 200 km h $^{-1}$ , and along DA 100 km h $^{-1}$ . Its average speed (in km h $^{-1}$ ) over the entire trip is

A

225.5

B

175.5

C

125.5

D

310.5

E

190.5

Question 93: Palette 93/238

Errorless DUMET 2009 MCQ

The three initial and final position of a man on the x-axis are given as (i) $(-8m,7m)$ (ii) $(7m,-3m)$ and (iii) $(-7m,3m)$ Which pair gives the negative displacement

A

(i)

B

(ii)

C

(iii)

D

(i) and (iii)

Question 94: Palette 94/238

Errorless AIEEE 2009; CBSE PMT 2010, 12 MCQ

A particle has an initial velocity of $3\hat{i} + 4\hat{j}$ 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 95: Palette 95/238

Errorless DCE 2009 MCQ

The acceleration $a$ of a particle starting from rest varies with time according to relation $a = \alpha t + \beta$ . The velocity of the particle after a time $t$ will be

A

$\frac{\alpha t^2}{2} + \beta$

B

$\frac{\alpha t^2}{2} + \beta t$

C

$\alpha t^2 + \frac{1}{2}\beta t$

D

$\frac{(\alpha t^2 + \beta)}{2}$

Question 96: Palette 96/238

Errorless Kerala PMT 2009 MCQ

A car starts from rest and accelerates uniformly to a speed of $180 \, kmh^{-1}$ in 10 seconds. The distance covered by the car in this time interval is

A

500 m

B

250 m

C

100 m

D

200 m

E

150 m

Question 97: Palette 97/238

Errorless DUMET 2009 MCQ

You drive a car at a speed of 70 km/hr in a straight road for 8.4 km, and then the car runs out of petrol. You walk for 30 min to reach a petrol pump at a distance of 2 km. The average velocity from the beginning of your drive till you reach the petrol pump is

A

16.8 km/hr

B

35 km/hr

C

64 km/hr

D

18.6 km/hr

Question 98: Palette 98/238

Errorless DUMET 2009 MCQ

A boat crosses a river from port $A$ to port $B$ , which are just on the opposite side. The speed of the water is $V_{W}$ and that of boat is $V_{B}$ relative to still water. Assume $V_{B} = 2V_{W}$ . What is the time taken by the boat, if it has to cross the river directly on the $AB$ line

A

$\frac{2D}{V_B\sqrt{3}}$

B

$\frac{\sqrt{3}D}{2V_B}$

C

$\frac{D}{V_B\sqrt{2}}$

D

$\frac{D\sqrt{2}}{V_B}$

Question 99: Palette 99/238

Errorless MP PMT 2009 MCQ

In figure, one car is at rest and velocity of light from head light is c, then velocity of light from head light for the moving car at velocity v, would be

A

$c + v$

B

c - v

C

$c \times v$

D

c

Question 100: Palette 100/238

Errorless Kerala PET 2009 MCQ

A ball $A$ is thrown up vertically with a speed $u$ and at the same instant another ball $B$ is released from a height $h$ . At time $t$ , the speed of $A$ relative to $B$ is

A

$u$

B

$2u$

C

$u - gt$

D

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

E

$gt$

Question 101: Palette 101/238

Errorless AMU (Engg.) 2009 MCQ

A body is thrown vertically up with a velocity $u$ . It passes three points $A, B$ and $C$ in its upward journey with velocities $\frac{u}{2}, \frac{u}{3}$ and $\frac{u}{4}$ respectively. The ratio of the separations between points $A$ and $B$ and between $B$ and $C$ i.e., $\frac{AB}{BC}$ is

A

1

B

2

C

$\frac{10}{7}$

D

$\frac{20}{7}$

Question 102: Palette 102/238

Errorless KCET 2009; Kerala PET 2012 MCQ

A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

A

4.0 m/s

B

5.0 m/s

C

5.5 m/s

D

4.8 m/s

Question 103: Palette 103/238

Errorless MP PMT 2009 MCQ

Which graph represents a state of rest for an object

A

B

C

D

Question 104: Palette 104/238

Errorless DCE 2009 MCQ

A particle starts from rest at $t = 0$ and undergoes an acceleration a in $ms^{-2}$ with time $t$ in seconds which is as shown. Which one of the following plot represents velocity V in $ms^{-1}$ versus time t in seconds

A

B

C

D

Question 105: Palette 105/238

Errorless J & K CET 2008 MCQ

A body is moving along a straight line path with constant velocity. At an instant of time the distance travelled by it is S and its displacement is D, then

A

D < S

B

D > S

C

D = S

D

D ≤ S

Question 106: Palette 106/238

Errorless WB-JEE 2008 MCQ

A bullet emerges from a barrel of length $1.2 \, m$ with a speed of $640 \, ms^{-1}$ . Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired is

A

$4 \, ms$

B

$40 \, ms$

C

$400 \, \mu s$

D

$1 \, s$

Question 107: Palette 107/238

Errorless CBSE PMT 2008 MCQ

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10 \, ms^{-1}$ to $20 \, ms^{-1}$ while passing through a distance 135 m in t second. The value of t is

A

12

B

9

C

10

D

1.8

Question 108: Palette 108/238

Errorless Kerala PET 2008 MCQ

A particle starts from rest at $t = 0$ and moves in a straight line with an acceleration as shown below. The velocity of the particle at $t = 3 \, \text{s}$ is

A

$2ms^{-1}$

B

$4ms^{-1}$

C

$6ms^{-1}$

D

$8ms^{-1}$

E

$1ms^{-1}$

Question 109: Palette 109/238

Errorless Kerala PET 2008 MCQ

Two cars A and B are moving with same speed of 45 km/hr along same direction. If a third car C coming from the opposite direction with a speed of 36 km/hr meets two cars in an interval of 5 minutes, the distance of separation of two cars A and B should be (in km)

A

6.75

B

7.25

C

5.55

D

8.35

E

4.75

Question 110: Palette 110/238

Errorless Kerala PMT 2008 MCQ

Two bodies are thrown vertically upwards with their initial speed in the ratio 2:3. The ratio of the maximum heights reached by them and the ratio of their time taken by them to return back to the ground respectively are

A

4:9 and 2:3

B

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

C

$\sqrt{2}:\sqrt{3}$ and $4:9$

D

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

E

4:9 and $3:2$

Question 111: Palette 111/238

Errorless AIEEE 2008 MCQ

A body is a rest at $x = 0$ . At $t = 0$ , it starts moving in the positive $x$ -direction with a constant acceleration. At the same instant another body passes through $x = 0$ moving in the positive $x$ -direction with a constant speed. The position of the first body is given by $x_{1}(t)$ after time 't' and that of the second body by $x_{2}(t)$ after the same time interval. Which of the following graphs correctly describes $(x_{1} - x_{2})$ as a function of time 't'

A

B

C

D

Question 112: Palette 112/238

Errorless Kerala PET 2008 MCQ

An object is dropped from rest. Its $v - t$ graph is

A

B

C

D

E

Question 113: Palette 113/238

Errorless CBSE PMT 2008 MCQ

A particle shows distance – time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point

A

D

B

A

C

B

D

C

Question 114: Palette 114/238

Errorless J & K CET 2008 MCQ

A body starts from rest and moves with uniform acceleration. Which of the following graphs represent its motion

A

B

C

D

Question 115: Palette 115/238

Errorless KCET 2008 MCQ

A particle is projected upwards. The times corresponding to height h while ascending and while descending are $t_{1}$ and $t_{2}$ respectively. The velocity of projection will be

A

$g t_{1}$

B

$g t_{2}$

C

$g (t_{1} + t_{2})$

D

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

Question 116: Palette 116/238

Errorless Kerala PMT 2007; CBSE PMT 2009; MP PET 2011; KCET 2012 MCQ

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is $S_{1}$ and that covered in the first 20 seconds is $S_{2}$ , then

A

$S_{2} = 2S_{1}$

B

$S_{2} = 3S_{1}$

C

$S_{2} = 4S_{1}$

D

$S_{2} = S_{1}$

Question 117: Palette 117/238

Errorless AIEEE 2007; JEE (Main) 2021 MCQ

The velocity of a particle is $v = v_{0} + gt + ft^{2}$ . If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

A

$v_{0} + 2g + 3f$

B

$v_{0} + g/2 + f/3$

C

$v_{0} + g + f$

D

$v_{0} + g/2 + f$

Question 118: Palette 118/238

Errorless MP PET 2007 MCQ

A body starts from rest. What is the ratio of the distance travelled by the body during the $4^{\text{th}}$ and 3rd second

A

$\frac{7}{5}$

B

$\frac{5}{7}$

C

$\frac{7}{3}$

D

$\frac{3}{7}$

Question 119: Palette 119/238

Errorless CBSE PMT 2007 MCQ

The position x of a particle with respect to time t along x-axis is given by $x = 9t^{2} - t^{3}$ where x is in metres and t in second. What will be the position of this particle when it achieves maximum speed along the +x direction

A

32 m

B

54 m

C

81 m

D

24 m

Question 120: Palette 120/238

Errorless Kerala PET 2007 MCQ

Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed u along the track so that the relative velocities of the trains with respect to the wind are in the ratio 1:2, then the speed of each train must be

A

3u

B

2u

C

5u

D

4u

Question 121: Palette 121/238

Errorless Kerala PET 2007; Odisha JEE 2008, 12 MCQ

A ball falls from height h. After 1 second, another ball falls freely from a point 20 m below the point from where the first ball falls. Both of them reach the ground at the same time. What is the value of h

A

11.2 m

B

21.2 m

C

31.2 m

D

41.2 m

Question 122: Palette 122/238

Errorless KCET 2006 MCQ

A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is

A

0, 1

B

$\frac{\pi+4}{2}$ , 0

C

21.4, $\frac{\pi+4}{2}$

D

0, 21.4

Question 123: Palette 123/238

Errorless AFMC 2006; WB-JEE 2012 MCQ

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by $x = 40 + 12t - t^{3}$ How long would the particle travel before coming to rest

A

24 m

B

40 m

C

56 m

D

16 m

Question 124: Palette 124/238

Errorless J & K CET 2006 MCQ

From a balloon rising vertically upwards at $5m / s$ a stone is thrown up at $10m / s$ relative to the balloon. Its velocity with respect to ground after $2s$ is (assume $g = 10m / s^2$ )

A

0

B

$20m / s$

C

$10m / s$

D

$5m / s$

Question 125: Palette 125/238

Errorless MP PET 2006; Kerala PET 2007 MCQ

A balloon is at a height of 81 m and is ascending upwards with a velocity of 12 m/s. A body of 2kg weight is dropped from it. If $g=10m/s^{2}$ , the body will reach the surface of the earth in

A

1.5 s

B

4.025 s

C

5.4 s

D

6.75 s

Question 126: Palette 126/238

Errorless AIEEE 2006 MCQ

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as $v = \alpha\sqrt{x}$ . The displacement of the particle varies with time as

A

t

B

$t^{1/2}$

C

$t^{3}$

D

$t^{2}$

Question 127: Palette 127/238

Errorless UP CPMT 2006 MCQ

A point initially at rest moves along x-axis. Its acceleration varies with time as $a = (6t + 5)m/s^{2}$ . If it starts from origin, the distance covered in 2 s is

A

20 m

B

18 m

C

16 m

D

25 m

Question 128: Palette 128/238

Errorless KCET 2006 MCQ

Look at the graphs (a) to (d) carefully and indicate which of these possibly represents one dimensional motion of a particle

A

B

C

D

Question 129: Palette 129/238

Errorless BHU 2006 MCQ

A boy begins to walk eastward along a street in front of his house and the graph of his position from home is shown in the following figure. His average speed for the whole time interval is equal to

A

$8m / \mathrm{min}$

B

$6m / \min$

C

$\frac{8}{3} m / \min$

D

$2m / \min$

Question 130: Palette 130/238

Errorless MP PET 2006 MCQ

$v - t$ graph for a particle is as shown. The distance travelled in the first 4s is $V(m / s)$

A

12m

B

16m

C

20m

D

24m

Question 131: Palette 131/238

Errorless CBSE PMT 2005 MCQ

Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity $v_{1}$ . The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is

A

$a/\sqrt{v^{2} + v_{1}^{2}}$

B

$\sqrt{a^{2}/(v^{2} - v_{1}^{2})}$

C

$a/(v - v_{1})$

D

$a/(v + v_{1})$

Question 132: Palette 132/238

Errorless RPMT 2005 MCQ

A body moves for a total of nine second starting from rest with uniform acceleration and then with uniform retardation, which is twice the value of acceleration and then stops. The duration of uniform acceleration

A

$3s$

B

$4.5s$

C

$5s$

D

$6s$

Question 133: Palette 133/238

Errorless AIEEE 2005; BCECE 2006; MP PET 2012; JEE (Main) 2021 MCQ

The relation between time and distance is $t = \alpha x^{2} + \beta x$ , where $\alpha$ and $\beta$ are constants. The retardation is

A

$2\alpha v^{3}$

B

$2\beta v^{3}$

C

$2\alpha\beta v^{3}$

D

$2\beta^{2}v^{3}$

Question 134: Palette 134/238

Errorless AFMC 2005 MCQ

What determines the nature of the path followed by the particle

A

Speed

B

Velocity

C

Acceleration

D

Both a and b

Question 135: Palette 135/238

Errorless Kerala PET 2005 MCQ

A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th sec to that covered in 5 sec is

A

9/25

B

3/5

C

25/9

D

1/25

Question 136: Palette 136/238

Errorless AIEEE 2005 MCQ

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion

A

1.5 cm

B

1.0 cm

C

3.0 cm

D

2.0 cm

Question 137: Palette 137/238

Errorless AIEEE 2005; AIIMS 2008 MCQ

A car, starting from rest, accelerates at the rate $f$ through a distance $S$ , then continues at constant speed for time $t$ and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is 15 $S$ , then

A

$S = \frac{1}{2} ft^2$

B

$S = \frac{1}{4} ft^2$

C

$S = \frac{1}{72} ft^2$

D

$S = \frac{1}{6} ft^2$

Question 138: Palette 138/238

Errorless CBSE PMT 2005; BHU 2006 MCQ

The displacement $x$ of a particle varies with time $t$ , $x = ae^{-\alpha t} + be^{\beta t}$ , where $a, b, \alpha$ and $\beta$ are positive constants. The velocity of the particle will

A

Go on decreasing with time

B

Be independent of $\alpha$ and $\beta$

C

Drop to zero when $\alpha = \beta$

D

Go on increasing with time

Question 139: Palette 139/238

Errorless J & K CET 2005 MCQ

A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip is

A

5 min

B

60 min

C

20 min

D

30 min

Question 140: Palette 140/238

Errorless BHU 2005 MCQ

A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south

A

30° with downstream

B

60° with downstream

C

120° with downstream

D

South

Question 141: Palette 141/238

Errorless AIIMS 2005 MCQ

When a ball is thrown up vertically with velocity $V_{0}$ , it reaches a maximum height of 'h'. If one wishes to triple the maximum height then the ball should be thrown with velocity

A

$\sqrt{3}V_{0}$

B

$3V_{0}$

C

$9V_{0}$

D

$3/2V_{0}$

Question 142: Palette 142/238

Errorless KCET 2005 MCQ

From the top of a tower two stones, whose masses are in the ratio 1:2 are thrown one straight up with an initial speed u and the second straight down with the same speed u. Then, neglecting air resistance

A

The heavier stone hits the ground with a higher speed

B

The lighter stone hits the ground with a higher speed

C

Both the stones will have the same speed when they hit the ground

D

The speed can't be determined with the given data

Question 143: Palette 143/238

Errorless AIEEE 2005; AIIMS 2008 MCQ

A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at $2 \, m/s^{2}$ . He reaches the ground with a speed of 3 m/s. At what height, did he bail out

A

293 m

B

111 m

C

91 m

D

182 m

Question 144: Palette 144/238

Errorless Kerala PET 2005 MCQ

The area under acceleration-time graph gives

A

Distance travelled

B

Change in acceleration

C

Force acting

D

Change in velocity

Question 145: Palette 145/238

Errorless IIT-JEE (Screening) 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 146: Palette 146/238

Errorless J & K CET 2004 MCQ

A person moves 30 m north and then 20 m towards east and finally $30\sqrt{2}$ m in south-west direction. The displacement of the person from the origin will be

A

10 m along north

B

10 m long south

C

10 m along west

D

Zero

Question 147: Palette 147/238

Errorless Kerala PMT 2004 MCQ

An athlete completes one round of a circular track of radius R in 40 sec. What will be his displacement at the end of 2 min. 20 sec

A

Zero

B

2R

C

$2\pi R$

D

$7\pi R$

Question 148: Palette 148/238

Errorless MH CET 2004 MCQ

A particle moves for 20 seconds with velocity $3\mathrm{m / s}$ and then velocity $4\mathrm{m / s}$ for another 20 seconds and finally moves with velocity $5\mathrm{m / s}$ for next 20 seconds. What is the average velocity of the particle

A

$3\mathrm{m / s}$

B

$4\mathrm{m / s}$

C

$5\mathrm{m / s}$

D

Zero

Question 149: Palette 149/238

Errorless DCE 2004 MCQ

Which of the following options is correct for the object having a straight line motion represented by the following graph

A

The object moves with constantly increasing velocity from $O$ to $A$ and then it moves with constant velocity.

B

Velocity of the object increases uniformly

C

Average velocity is zero

D

The graph shown is impossible

Question 150: Palette 150/238

Errorless J & K CET 2004; Odisha JEE 2012 MCQ

If the velocity of a particle is given by $v = (180 - 16x)^{1/2}$ m/s, then its acceleration will be

A

Zero

B

$8 \, m/s^{2}$

C

$-8 \, m/s^{2}$

D

$4 \, m/s^{2}$

Question 151: Palette 151/238

Errorless BCECE 2004 MCQ

An object accelerates from rest to a velocity 27.5 m/s in 10 sec then find distance covered by object in next 10 sec

A

550 m

B

137.5 m

C

412.5 m

D

275 m

Question 152: Palette 152/238

Errorless MP PMT 2004 MCQ

A car starts from rest and moves with uniform acceleration $a$ on a straight road from time $t = 0$ to $t = T$ . After that, a constant deceleration brings it to rest. In this process the average speed of the car is

A

$\frac{aT}{4}$

B

$\frac{3aT}{2}$

C

$\frac{aT}{2}$

D

$aT$

Question 153: Palette 153/238

Errorless J & K CET 2004 MCQ

A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is

A

East-north direction

B

West-north direction

C

South-east direction

D

None of these

Question 154: Palette 154/238

Errorless UPSEAT 2004 MCQ

A body is thrown vertically upwards with velocity u. The distance travelled by it in the fifth and the sixth seconds are equal. The velocity u is given by $(g = 9.8 \, m/s^{2})$

A

24.5 m/s

B

49.0 m/s

C

73.5 m/s

D

98.0 m/s

Question 155: Palette 155/238

Errorless Pb. PMT 2004 MCQ

The effective acceleration of a body, when thrown upwards with acceleration $a$ will be

A

$\sqrt{a - g^2}$

B

$\sqrt{a^2 + g^2}$

C

$(a - g)$

D

$(a + g)$

Question 156: Palette 156/238

Errorless Pb. PMT 2004 MCQ

A packet is dropped from a balloon which is going upwards with the velocity 12 m/s, the velocity of the packet after 2 seconds will be

A

-12 m/s

B

12 m/s

C

-7.6 m/s

D

7.6 m/s

Question 157: Palette 157/238

Errorless AIEEE 2004 MCQ

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds

A

h/9 meters from the ground

B

7h/9 meters from the ground

C

8h/9 meters from the ground

D

17h/18 meters from the ground

Question 158: Palette 158/238

Errorless IIT-JEE (Screening) 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 m/s

B

55 m/s

C

550 m/s

D

660 m/s

Question 159: Palette 159/238

Errorless IIT-JEE (Screening) 2004; NEET 2021 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 160: Palette 160/238

Errorless AIIMS 2004 MCQ

Which of the following velocity-time graphs shows a realistic situation for a body in motion

A

B

C

D

Question 161: Palette 161/238

Errorless Kerala PMT 2004 MCQ

Which of the following velocity-time graphs represent uniform motion

A

B

C

D

Question 162: Palette 162/238

Errorless DPMT 2004 MCQ

Acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is

A

B

C

D

Question 163: Palette 163/238

Errorless MP PMT 2003 MCQ

If a car covers $2/5^{th}$ of the total distance with $v_{1}$ speed and $3/5^{th}$ distance with $v_{2}$ then average speed is

A

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

B

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

C

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

D

$\frac{5v_{1}v_{2}}{3v_{1}+2v_{2}}$

Question 164: Palette 164/238

Errorless KCET 2003; J & K CET 2005 MCQ

A man is 45 m behind the bus when the bus start accelerating from rest with acceleration $2.5 \, m/s^{2}$ . With what minimum velocity should the man start running to catch the bus

A

12 m/s

B

14 m/s

C

15 m/s

D

16 m/s

Question 165: Palette 165/238

Errorless Pb. PET 2003 MCQ

A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in next 5 sec. Its initial velocity will be

A

4 m/s

B

2.5 m/s

C

5.5 m/s

D

11 m/s

Question 166: Palette 166/238

Errorless MP PET 2003 MCQ

A body $A$ moves with a uniform acceleration $a$ and zero initial velocity. Another body $B$ , starts from the same point moves in the same direction with a constant velocity $v$ . The two bodies meet after a time $t$ . The value of $t$ is

A

$\frac{2v}{a}$

B

$\frac{v}{a}$

C

$\frac{v}{2a}$

D

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

Question 167: Palette 167/238

Errorless BHU 2003; CPMT 2004; RPMT 2006; AMU (Engg.) 2012 MCQ

A police jeep is chasing with velocity of 45 km/h a thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity with which it will strike the car of the thief is

A

150 m/s

B

27 m/s

C

450 m/s

D

250 m/s

Question 168: Palette 168/238

Errorless RPET 2003 MCQ

A stone thrown upward with a speed u from the top of the tower reaches the ground with a velocity 3u. The height of the tower is

A

$3u^{2}/g$

B

$4u^{2}/g$

C

$6u^{2}/g$

D

$9u^{2}/g$

Question 169: Palette 169/238

Errorless MH CET 2003; Pb. PMT 2004; WB-JEE 2010 MCQ

If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three second, the time of the travel is

A

6 sec

B

5 sec

C

4 sec

D

3 sec

Question 170: Palette 170/238

Errorless CBSE PMT 2003 MCQ

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given $g = 9.8m / s^2$ )

A

At least $0.8\,m/s$

B

Any speed less than $19.6\,m/s$

C

Only with speed $19.6\,m/s$

D

More than $19.6\,m/s$

Question 171: Palette 171/238

Errorless CBSE PMT 2003 MCQ

If a ball is thrown vertically upwards with speed $u$ , the distance covered during the last $t$ seconds of its ascent is

A

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

B

$ut - \frac{1}{2} gt^2$

C

$(u - gt)t$

D

$ut$

Question 172: Palette 172/238

Errorless AIIMS 2003 MCQ

A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its flight if the air resistance is not ignored

A

B

C

D

Question 173: Palette 173/238

Errorless DCE 2003, 09; WB-JEE 2009 MCQ

Which graph represents the uniform acceleration

A

B

C

D

Question 174: Palette 174/238

Errorless AMU (Med.) 2002 MCQ

A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km/h. The average speed of the man over the interval of time 0 to 40 min. is equal to

A

5 km/h

B

$\frac{25}{4}$ km/h

C

$\frac{30}{4}$ km/h

D

$\frac{45}{8}$ km/h

Question 175: Palette 175/238

Errorless PET 2002; BHU 2004 MCQ

The numerical ratio of displacement to the distance covered is always

A

Less than one

B

Equal to one

C

Equal to or less than one

D

Equal to or greater than one

Question 176: Palette 176/238

Errorless MP PET 2002 MCQ

The path of a particle moving under the influence of a force fixed in magnitude and direction is

A

Straight line

B

Circle

C

Parabola

D

Ellipse

Question 177: Palette 177/238

Errorless Pb. PMT 2002 MCQ

The engine of a motorcycle can produce a maximum acceleration $5 \, m/s^{2}$ . Its brakes can produce a maximum retardation $10 \, m/s^{2}$ . What is the minimum time in which it can cover a distance of 1.5 km

A

30 sec

B

15 sec

C

10 sec

D

5 sec

Question 178: Palette 178/238

Errorless RPET 2002; WB-JEE 2009 MCQ

Starting from rest, acceleration of a particle is $a = 2(t - 1)$ . The velocity of the particle at t = 5s is

A

15 m/sec

B

25 m/sec

C

5 m/sec

D

None of these

Question 179: Palette 179/238

Errorless RPET 2002 MCQ

An express train is moving with a velocity $v_{1}$ . Its driver finds another train is moving on the same track in the same direction with velocity $v_{2}$ . To escape collision, driver applies a retardation a on the train. the minimum time of escaping collision will be

A

$t = \frac{v_{1} - v_{2}}{a}$

B

$t = \frac{v_{1}^{2} - v_{2}^{2}}{2}$

C

None

D

Both

Question 180: Palette 180/238

Errorless Kerala PMT 2002 MCQ

A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is

A

4.9 m

B

9.8 m

C

19.6 m

D

24.5 m

Question 181: Palette 181/238

Errorless MP PMT 2002; MP PET 2006 MCQ

A body falling from a high Minaret travels 40 m in the last 2 seconds of its fall to ground. Height of Minaret in meters is (take $g = 10m/s^{2}$ )

A

60

B

45

C

80

D

50

Question 182: Palette 182/238

Errorless KCET 2002 MCQ

A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is $5m$ , the number of ball thrown per minute is (take $g = 10ms^{-2}$ )

A

120

B

80

C

60

D

40

Question 183: Palette 183/238

Errorless Kerala PMT 2002; MP PMT 2003 MCQ

A cricket ball is thrown up with a speed of $19.6 \, ms^{-1}$ . The maximum height it can reach is

A

9.8 m

B

19.6 m

C

29.4 m

D

39.2 m

Question 184: Palette 184/238

Errorless Odisha JEE 2002; CPMT 2003 MCQ

A ball is dropped from top of a tower of 100m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of 50 m/s ( $g = 10m/s^{2}$ ). They will cross each other after

A

1s

B

2s

C

3s

D

4s

Question 185: Palette 185/238

Errorless AIEEE 2002; Odisha JEE 2009 MCQ

Two balls A and B of same masses are thrown from the top of the building. A, thrown upward with velocity V and B, thrown downward with velocity V, then

A

Velocity of A is more than B at the ground

B

Velocity of B is more than A at the ground

C

Both A & B strike the ground with same velocity

D

None of these

Question 186: Palette 186/238

Errorless AIIMS 2002 MCQ

Three different objects of masses $m_{1}, m_{2}$ and $m_{3}$ are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of

A

$m_{1}: m_{2}: m_{3}$

B

$m_{1}: 2m_{2}: 3m_{3}$

C

1:1:1

D

$\frac{1}{m_{1}}: \frac{1}{m_{2}}: \frac{1}{m_{3}}$

Question 187: Palette 187/238

Errorless MP PMT 2001; CBSE PMT 2007; CBSE PMT (Mains) 2011 MCQ

A cat moves from X to Y with a uniform speed $v_{u}$ and returns to X with a uniform speed $v_{d}$ . The average speed for this round trip is

A

$\frac{2v_{d}v_{u}}{v_{d}+v_{u}}$

B

$\sqrt{v_{u}v_{d}}$

C

$\frac{v_{d}v_{u}}{v_{d}+v_{u}}$

D

$\frac{v_{u}+v_{d}}{2}$

Question 188: Palette 188/238

Errorless CBSE PMT 2001; BHU 2004 MCQ

A 150 m long train is moving with a uniform velocity of 45 km/h. The time taken by the train to cross a bridge of length 850 m is

A

56 sec

B

68 sec

C

80 sec

D

92 sec

Question 189: Palette 189/238

Errorless AIIMS 2001; RPMT 2006 MCQ

The velocity of a bullet is reduced from 200m/s to 100m/s while travelling through a wooden block of thickness 10cm. The retardation, assuming it to be uniform, will be

A

$10 \times 10^{4}$ m/s $^{2}$

B

$12 \times 10^{4}$ m/s $^{2}$

C

$13.5 \times 10^{4}$ m/s $^{2}$

D

$15 \times 10^{4}$ m/s $^{2}$

Question 190: Palette 190/238

Errorless AIIMS 2001 MCQ

A body $A$ starts from rest with an acceleration $a_1$ . After 2 seconds, another body $B$ starts from rest with an acceleration $a_2$ . If they travel equal distances in the 5th second, after the start of $A$ , then the ratio $a_1: a_2$ is equal to

A

5:9

B

5:7

C

9:5

D

9:7

Question 191: Palette 191/238

Errorless DCE 2001, 03; AIIMS 2002 MCQ

A particle starts from rest, accelerates at $2 \, m/s^{2}$ for 10s and then goes with constant speed for 30s and then decelerates at $4 \, m/s^{2}$ till it stops. What is the distance travelled by it

A

750 m

B

800 m

C

700 m

D

850 m

Question 192: Palette 192/238

Errorless CPMT 2001; Pb. PET 2004; AMU (Engg.) 2012 MCQ

A boat is sent across a river with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is

A

10 km/hr

B

8 km/hr

C

6 km/hr

D

4 km/hr

Question 193: Palette 193/238

Errorless CBSE PMT 2001, 04; KCET 2001; BHU 2004 MCQ

A body, thrown upwards with some velocity, reaches the maximum height of 20m. Another body with double the mass thrown up, with double initial velocity will reach a maximum height of

A

200 m

B

16 m

C

80 m

D

40 m

Question 194: Palette 194/238

Errorless KCET 2001 MCQ

A balloon starts rising from the ground with an acceleration of $1.25 \, m/s^2$ after 8s, a stone is released from the balloon. The stone will ( $g = 10 \, m/s^2$ )

A

Reach the ground in 4 second

B

Begin to move down after being released

C

Have a displacement of $50 \, m$

D

Cover a distance of $40 \, m$ in reaching the ground

Question 195: Palette 195/238

Errorless DCE 2001, 09 MCQ

The graph of displacement v/s time is Its corresponding velocity-time graph will be

A

B

C

D

Question 196: Palette 196/238

Errorless CPMT 2000; NEET (Karnataka) 2013 MCQ

The relation $3t = \sqrt{3x} + 6$ describes the displacement of a particle in one direction where x is in metres and t in sec. The displacement, when velocity is zero, is

A

24 metres

B

12 metres

C

5 metres

D

Zero

Question 197: Palette 197/238

Errorless EAMCET (Engg.) 2000 MCQ

A body thrown vertically upwards with an initial velocity $u$ reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is

A

1:1

B

11:1

C

1:2

D

1:11

Question 198: Palette 198/238

Errorless AMU (Engg.) 2000; J & K CET 2010; JEE (Main) 2017 MCQ

A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)
(A)

(B)

(C)

(D)

A

A

B

B

C

C

D

D

Question 199: Palette 199/238

Errorless KCET 1999; JIPMER 1999; DCE 2000; AFMC 2003, 04 MCQ

An aeroplane flies 400 m north and 300 m south and then flies 1200 m upwards then net displacement is

A

1200 m

B

1300 m

C

1400 m

D

1500 m

Question 200: Palette 200/238

Errorless MP PET 1999, 2001; Pb. PET 2003 MCQ

The displacement-time graph for two particles A and B are straight lines inclined at angles of $30^{\circ}$ and $60^{\circ}$ with the time axis. The ratio of velocities of $V_{A}:V_{B}$ is

A

1:2

B

$1:\sqrt{3}$

C

$\sqrt{3}:1$

D

1:3

Question 201: Palette 201/238

Errorless RPMT 1999; AFMC 1999, 2006; BHU 2000; AMU (Med.) 2000; CPMT 2001; Odisha JEE 2009 MCQ

The motion of a particle is described by the equation $ x = a + b t ^ {2}$ where a=15cm and $ b = 3 \quad c m / s ^ {2}$. Its instantneous velocity at time sec will be

A

36 cm/sec

B

18 cm/sec

C

16 cm/sec

D

32 cm/sec

Question 202: Palette 202/238

Errorless RPMT 1999, 06; RPET 2002; CPMT 2003; CBSE PMT 2006 MCQ

Two bodies of different masses $m_{a}$ and $m_{b}$ are dropped from two different heights a and b. The ratio of the time taken by the two to cover these distances are

A

a:b

B

b:a

C

$\sqrt{a}:\sqrt{b}$

D

$a^{2}:b^{2}$

Question 203: Palette 203/238

Errorless KCET 1999; Pb. PMT 2000; RPMT 2006 MCQ

A body projected vertically upwards with a velocity $u$ returns to the starting point in 4 seconds. If $g = 10\mathrm{m / sec}^2$ , the value of $u$ is

A

$5\mathrm{m / sec}$

B

$10\mathrm{m / sec}$

C

$15\mathrm{m / sec}$

D

$20\mathrm{m / sec}$

Question 204: Palette 204/238

Errorless AFMC 1999; Pb. PMT 2003; KCET 2004 MCQ

A stone is thrown with an initial speed of 4.9 m/s from a bridge in vertically upward direction. It falls down in water after 2 sec. The height of the bridge is

A

4.9 m

B

9.8 m

C

19.8 m

D

24.7 m

Question 205: Palette 205/238

Errorless CBSE PMT 1998, 99; AFMC 2000; JIPMER 2001, 02; AIEEE 2002, 03, 04 MCQ

A car moving with a speed of 40 km/h can be stopped by applying brakes after atleast 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance

A

8 m

B

2 m

C

4 m

D

6 m

Question 206: Palette 206/238

Errorless CPMT 1998; Pb. PET 2002 MCQ

A boat is moving with a velocity $3i + 4j$ with respect to ground. The water in the river is moving with a velocity - 3i - 4j with respect to ground. The relative velocity of the boat with respect to water is

A

8j

B

- 6i - 8j

C

6i + 8j

D

$5\sqrt{2}$

Question 207: Palette 207/238

Errorless SCRA 1998; DCE 2000; AIIMS 2003; Odisha PMT 2004 MCQ

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement (s) - velocity (v) graph of this object is

A

B

C

D

Question 208: Palette 208/238

Errorless CBSE PMT 1997; BHU 1999; DPMT 2000; KCET 2000; JIPMER 2001, 02; AMU (Engg.) 2009; WB-JEE 2013 MCQ

A particle moves along a straight line such that its displacement at any time t is given by $S = t^{3} - 6t^{2} + 3t + 4$ metres The velocity when the acceleration is zero is

A

$3ms^{-1}$

B

$-12ms^{-1}$

C

$42ms^{-1}$

D

$-9ms^{-1}$

Question 209: Palette 209/238

Errorless CPMT 1997; BHU 1998; DPMT 1999; RPET 1999; MH CET 2003 MCQ

A stone dropped from the top of the tower touches the ground in 4 sec. The height of the tower is about

A

80 m

B

40 m

C

20 m

D

160 m

Question 210: Palette 210/238

Errorless CPMT 1997; AIIMS 2000; MH CET 2000; CBSE PMT 2002; MP PET 2003 MCQ

With what velocity a ball be projected vertically so that the distance covered by it in $5^{\text{th}}$ second is twice the distance it covers in its $6^{\text{th}}$ second ( $g = 10\,m/s^{2}$ )

A

58.8 m/s

B

49 m/s

C

65 m/s

D

19.6 m/s

Question 211: Palette 211/238

Errorless CPMT 1997; UPSEAT 2002; KCET 2002 MCQ

A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after $t_{1}$ and $t_{2}$ seconds respectively, then

A

$t = t_{1} - t_{2}$

B

$t = \frac{t_{1} + t_{2}}{2}$

C

$t = \sqrt{t_{1}t_{2}}$

D

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

Question 212: Palette 212/238

Errorless RPET 1996, 99; BHU 2002; MP PET 2009 MCQ

A person travels along a straight road for the first half time with a velocity $v_{1}$ and the next half time with a velocity $v_{2}$ . The mean velocity V of the man is

A

$\frac{2}{V} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

B

$V = \frac{v_{1} + v_{2}}{2}$

C

$V = \sqrt{v_{1}v_{2}}$

D

$V = \sqrt{\frac{v_{1}}{v_{2}}}$

Question 213: Palette 213/238

Errorless MP PMT 1996; CBSE PMT 2008 MCQ

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3} ms^{-2}$ , in the third second is

A

$\frac{10}{3} m$

B

$\frac{19}{3} m$

C

$6m$

D

$4m$

Question 214: Palette 214/238

Errorless MP PET 1996; CPMT 1999, 2003; Pb. PET 2004; J & K CET 2005; RPMT 2006; WB-JEE 2008; AMU (Engg.) 2012 MCQ

The displacement of a particle is given by $y = a + bt + ct^{2} - dt^{4}$ . The initial velocity and acceleration are respectively

A

b, -4d

B

-b, 2c

C

b, 2c

D

2c, -4d

Question 215: Palette 215/238

Errorless CPMT 1996; BHU 1998; CPMT 1999; JIPMER 2000; AMU (Med.) 2001; RPET 2001, 05; Kerala PET 2002; Kerala PMT 2008 MCQ

Two trains, each 50 m long are travelling in opposite direction with velocity 10 m/s and 15 m/s. The time of crossing is

A

2s

B

4s

C

$2\sqrt{3}s$

D

$4\sqrt{3}s$

Question 216: Palette 216/238

Errorless Kurukshetra CEE 1996; Kerala PMT 2006 MCQ

A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of 1 m each will then be

A

All equal, being equal to $\sqrt{2/g}$ second

B

In the ratio of the square roots of the integers 1, 2, 3......

C

In the ratio of the difference in the square roots of the integers i.e. $\sqrt{1}, (\sqrt{2} - \sqrt{1}), (\sqrt{3} - \sqrt{2}), (\sqrt{4} - \sqrt{3})$ ....

D

In the ratio of the reciprocal of the square roots of the integers i.e., $\frac{1}{\sqrt{1}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{4}}$

Question 217: Palette 217/238

Errorless Kurukshetra CEE 1996; DCE 2006 MCQ

Figures (i) and (ii) below show the displacement-time graphs of two particles moving along the x-axis. We can say that
(i)

(ii)

A

Both the particles are having a uniformly accelerated motion

B

Both the particles are having a uniformly retarded motion

C

Particle (i) is having a uniformly accelerated motion while particle (ii) is having a uniformly retarded motion

D

Particle (i) is having a uniformly retarded motion while particle (ii) is having a uniformly accelerated motion

Question 218: Palette 218/238

Errorless Manipal MEE 1995; AFMC 1998; MP PMT 1999; CPMT 2002; Kerala PMT 2005, 10 MCQ

A car travels half the distance with constant velocity of 40 kmph and the remaining half with a constant velocity of 60 kmph. The average velocity of the car in kmph is

A

40

B

45

C

48

D

50

Question 219: Palette 219/238

Errorless EAMCET (Engg.) 1995; CBSE PMT 2000; Kerala PET 2010 MCQ

Equation of displacement for any particle is $s = 3t^{3} + 7t^{2} + 14t + 8m$ . Its acceleration at time t = 1 sec is

A

$10 \, m/s^{2}$

B

$16 \, m/s^{2}$

C

$25 \, m/s^{2}$

D

$32 \, m/s^{2}$

Question 220: Palette 220/238

Errorless CBSE PMT 1995; MP PMT 2004 MCQ

A body is released from the top of a tower of height h. It takes t sec to reach the ground. Where will be the ball after time t/2 sec

A

At h/2 from the ground

B

At h/4 from the ground

C

Depends upon mass and volume of the body

D

At 3h/4 from the ground

Question 221: Palette 221/238

Errorless EAMCET (Med.) 1995; AIIMS 1999; Pb. PMT 2004; BHU 2004 MCQ

Velocity-time curve for a body projected vertically upwards is

A

Parabola

B

Ellipse

C

Hyperbola

D

Straight line

Question 222: Palette 222/238

Errorless MCQ

For a moving body at any instant of time

A

If the body is not moving, the acceleration is necessarily zero

B

If the body is slowing, the retardation is negative

C

If the body is slowing, the distance is negative

D

If displacement, velocity and acceleration at that instant are known, we can find the displacement at any given time in future

Question 223: Palette 223/238

Errorless MCQ

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4 \, ms^{-1}$ . The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take $g = 10 \, m \, s^{-2}$ )

A

60 m

B

64 m

C

68 m

D

56 m

Question 224: Palette 224/238

Errorless MCQ

Velocity-time $(v-t)$ graph for a moving object is shown in the figure. Total displacement of the object during the time interval when there is non-zero acceleration and retardation

A

60 m

B

50 m

C

30 m

D

40 m

Question 225: Palette 225/238

Errorless MCQ

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

A

B

C

D

Question 226: Palette 226/238

Errorless MCQ

If the velocity-time graph has the shape $AMB$ , what would be the shape of the corresponding acceleration-time graph

A

B

C

D

Question 227: Palette 227/238

Errorless MCQ

Assertion : A body can have acceleration even if its velocity is zero at a given instant of time. Reason : A body is momentarily at rest when it reverses its direction of motion.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 228: Palette 228/238

Errorless MCQ

Assertion : Two balls of different masses are thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed. Reason: The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 229: Palette 229/238

Errorless MCQ

Assertion : A body falling freely may do so with constant velocity. Reason : The body falls freely, when acceleration of a body is equal to acceleration due to gravity.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 230: Palette 230/238

Errorless MCQ

Assertion : An object can have constant speed but variable velocity. Reason : Speed is a scalar but velocity is a vector quantity.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 231: Palette 231/238

Errorless MCQ

A projectile is fired vertically upwards with an initial velocity $u$ . After an interval of $T$ seconds a second projectile is fired vertically upwards, also with initial velocity $u$

A

They meet at time $t = \frac{u}{g}$ and at a height $\frac{u^2}{2g} + \frac{gT^2}{8}$

B

They meet at time $t = \frac{u}{g} + \frac{T}{2}$ and at a height $\frac{u^2}{2g} + \frac{gT^2}{8}$

C

They meet at time $t=\frac{u}{g}+\frac{T}{2}$ and at a height $\frac{u^{2}}{2g}-\frac{gT^{2}}{8}$

D

They never meet

Question 232: Palette 232/238

Errorless MCQ

A particle moves along the sides $AB$ , $BC$ , $CD$ of a square of side $25m$ with a velocity of $15ms^{-1}$ . Its average velocity is

A

$1 5 m s ^ {- 1}$

B

$1 0 m s ^ {- 1}$

C

$7.5 m s ^ {- 1}$

D

$5 m s ^ {- 1}$

Question 233: Palette 233/238

Errorless MCQ

A body has speed V, 2V and 3V in first 1/3 of distance S, seconds 1/3 of S and third 1/3 of S respectively. Its average speed will be

A

V

B

2V

C

$\frac{18}{11}V$

D

$\frac{11}{18}V$

Question 234: Palette 234/238

Errorless MCQ

A body falls freely from the top of a tower. It covers 36% of the total height in the last second before striking the ground level. The height of the tower is

A

50 m

B

75 m

C

100 m

D

125 m

Question 235: Palette 235/238

Errorless MCQ

If the velocity of a particle is $(10 + 2t^{2})$ m/s, then the average acceleration of the particle between 2s and 5s is

A

$2 \, m/s^{2}$

B

$4 \, m/s^{2}$

C

$12 \, m/s^{2}$

D

$14 \, m/s^{2}$

Question 236: Palette 236/238

Errorless MCQ

A bullet moving with a velocity of $200 \mathrm{~cm} / \mathrm{s}$ penetrates a wooden block and comes to rest after traversing $4 \mathrm{~cm}$ inside it. What velocity is needed for travelling distance of $9 \mathrm{~cm}$ in same block

A

$100 \mathrm{~cm} / \mathrm{s}$

B

$136.2 \mathrm{~cm} / \mathrm{s}$

C

$300 \mathrm{~cm} / \mathrm{s}$

D

$250 \mathrm{~cm} / \mathrm{s}$

Question 237: Palette 237/238

Errorless MCQ

A car $A$ is travelling on a straight level road with a uniform speed of $60 \, \text{km/h}$ . It is followed by another car $B$ which is moving with a speed of $70 \, \text{km/h}$ . When the distance between them is $2.5 \, \text{km}$ , the car $B$ is given a deceleration of $20 \, \text{km/h}^2$ . After how much time will $B$ catch up with $A$

A

$1 \, \text{hr}$

B

$1/2 \, \text{hr}$

C

$1/4 \, \text{hr}$

D

$1/8 \, \text{hr}$

Question 238: Palette 238/238

Errorless MCQ

The speed of a body moving with uniform acceleration is u. This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

A

$\sqrt{3}u$

B

$\sqrt{5}u$

C

$\sqrt{11}u$

D

$\sqrt{7}u$