Question 1: Palette 1/112

Objective NEET 2020 MCQ

A person sitting in the ground floor of a building notices through the window of height 1.5 m, a ball dropped from the roof of the building crosses the window in 0.1 s. What is the velocity of the ball when it is at the topmost point of the window? (Take, $ g = 10 \, m/s^{2} $ )

A

$15.5\mathrm{m / s}$

B

$1.45\mathrm{m / s}$

C

$4.5\mathrm{m / s}$

D

$20\mathrm{m / s}$

Question 2: Palette 2/112

Objective NEXT 2019 MCQ

A person travelling in a straight line moves with a constant velocity $ v_{1} $ for certain distance $ x $ and with a constant velocity $ v_{2} $ for next equal distance. The average velocity $ v $ is given by the relation

A

$\frac{1}{v} = \frac{1}{v_1} +\frac{1}{v_2}$

B

$\frac{2}{v} = \frac{1}{v_1} +\frac{1}{v_2}$

C

$\frac{9}{2} = \frac{v_1 + v_2}{2}$

D

$v = \sqrt{v_1v_2}$

Question 3: Palette 3/112

Objective JIPMER 2019 MCQ

Find the average velocity when a particle complete the circle of radius 1m in 10 s,

A

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

B

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

C

$6.28\mathrm{ms}^{-1}$

D

Zero

Question 4: Palette 4/112

Objective JIPMER 2019 MCQ

Speed of a particle at 3rd and 8th second are $20\mathrm{ms}^{-1}$ and zero respectively, then average acceleration between 3rd and 8th second will be

A

$ 3 \, ms^{-2} $

B

$4\mathrm{ms}^{-2}$

C

$5\mathrm{ms}^{-2}$

D

$6\mathrm{ms}^{-2}$

Question 5: Palette 5/112

Objective 2018 MCQ

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force qE, its velocity increases from 0 to 6 ms $ ^{-1} $ in one second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 s are respectively (NEET 2018)

A

$1\mathrm{ms}^{-1},3.5\mathrm{ms}^{-1}$

B

$1\mathrm{ms}^{-1},3\mathrm{ms}^{-1}$

C

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

D

$1.5\mathrm{ms}^{-1},3\mathrm{ms}^{-1}$

Question 6: Palette 6/112

Objective AIMS 2018 MCQ

Assertion: A body is momentarily at rest at the instant, if it reverse the direction. Reason: A body cannot have acceleration, if its velocity is zero at a given instant of time.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 7: Palette 7/112

Objective AIMS 2018 MCQ

Velocity is given by $ v = 4t(1 - 2t) $ , then find the value of time at which velocity is maximum.

A

0.25 s

B

1 s

C

0.45 s

D

4 s

Question 8: Palette 8/112

Objective JPMER 2018 MCQ

A ball is thrown upwards with a speed $ u $ from a height $ h $ above the ground. The time taken by the ball to hit the ground is

A

$\sqrt{2h / g}$

B

$\sqrt{8h / g}$

C

$\frac{\sqrt{u^2 + 2gh}}{g}$

D

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

Question 9: Palette 9/112

Objective NEET 2017 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

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

C

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

D

$t_1 - t_2$

Question 10: Palette 10/112

Objective Manipal 2017 MCQ

Which of the following statements is true for a car moving on the road?

A

With respect to the frame of reference attached to the ground, the car is at rest.

B

With respect to the frame of reference attached to the person sitting in the car, the car is at rest.

C

With respect to the frame of reference attached to the person outside the car, the car is at rest.

D

None of the above

Question 11: Palette 11/112

Objective 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 (NEET 2016)

A

$3A + 7B$

B

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

C

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

D

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

Question 12: Palette 12/112

Objective CISE AIPMT 2015 MCQ

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

A

$-2t\beta^{2}x^{2 - n - 1}$

C

$-2\beta^{2}x^{-2n + 1}$

D

$-2\beta^{2}x^{-2n + 1}$
[CISE AIPMT 2015]

B

$-2t\beta^{2}x^{-4n + 1}$

Question 13: Palette 13/112

Objective AIMS 2015 MCQ

A ball is dropped from a bridge 122.5 m above a river. After the ball has been falling for 2s, a second ball is thrown straight down after it. What must be the initial velocity of the second ball, so that both ball hit the water at the same time?

A

$40\mathrm{ms}^{-1}$

B

$55.5\mathrm{ms}^{-1}$

C

$26.1\mathrm{ms}^{-1}$

D

$9.6\mathrm{ms}^{-1}$

Question 14: Palette 14/112

Objective UK PMT 2015 MCQ

A ball is thrown vertically upwards from the ground with a speed of $ 25.2 \, ms^{-1} $ . How long does it take to reach its highest point and how high does it rise? (Take, g = $ 9.8 \, ms^{-2} $ )

A

$2.75\mathrm{s},3.24\mathrm{m}$

B

$25.7\mathrm{s},3.42\mathrm{m}$

C

$2.57\mathrm{s},32.4\mathrm{m}$

D

$27.5\mathrm{s},3.42\mathrm{m}$

Question 15: Palette 15/112

Objective EAMCET 2015 MCQ

A vehicle moving with a constant acceleration from A to B in a straight line AB, has velocities u and v at A and B respectively. C is the mid-point of AB. If time taken to travel from A to C is twice the time taken to travel from C to B, then the velocity of the vehicle v at B is

A

5 u

B

6 u

C

7 u

D

8 u

Question 16: Palette 16/112

Objective Kerala CEE 2015 MCQ

The displacement of a particle as a function of time is shown in figure. It indicates that

A

the velocity of the particle is constant throughout

B

the acceleration of the particle is constant throughout

C

the particle starts with a constant velocity and is accelerated

D

the motion is retarded and finally the particle stops

Question 17: Palette 17/112

Objective Manipal 2015 MCQ

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

A

$200\mathrm{m}$

B

$300\mathrm{m}$

C

$500\mathrm{m}$

D

$250\mathrm{m}$

Question 18: Palette 18/112

Objective KCET 2015 MCQ

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

A

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

B

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

C

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

D

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

Question 19: Palette 19/112

Objective Kerala CEE 2014 MCQ

A ball thrown vertically upwards after reaching a maximum height h returns to the starting point after a time of 10 s. Its displacement after 5 s is

A

h

B

2h

C

10h

D

20h

E

5h

Question 20: Palette 20/112

Objective EAMCET 2014 MCQ

A police jeep is chasing with velocity of $ 45 \, km h^{-1} $ , a thief in another jeep moving with velocity $ 153 \, km h^{-1} $ . Police fires a bullet with muzzle velocity of $ 180 \, m s^{-1} $ . The velocity with which it will strike the car of the thief is

A

$150\mathrm{ms}^{-1}$

B

$27\mathrm{ms}^{-1}$

C

$450\mathrm{ms}^{-1}$

D

$250\mathrm{ms}^{-1}$

Question 21: Palette 21/112

Objective WB JEE 2014 MCQ

A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the 4th second compared to that in the 3rd second is

A

$33\%$

B

$40\%$

C

$66\%$

D

$77\%$

Question 22: Palette 22/112

Objective UK PMT 2014 MCQ

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

A

$40\mathrm{kmh}^{-1}$

B

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

C

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

D

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

Question 23: Palette 23/112

Objective EAMCET 2014 MCQ

A particle starts moving from rest with uniform acceleration. It travels a distance $ x $ in first 2 s and distance $ y $ in the next 2 s. Then,

A

$ y = 3x $

B

$ y = 4x $

C

$ y = x $

D

$ y = 2x $

Question 24: Palette 24/112

Objective EAMCET 2014 MCQ

At time $ t = 0 $, two bodies $ A $ and $ B $ are at the same point. $ A $ moves with constant velocity $ v $ and $ B $ starts from rest and moves with constant acceleration. Relative velocity of $ B $ w.r.t. $ A $ when the bodies meet each other is

A

$\frac{v}{2}$

B

$\frac{v}{3}$

C

$v$

D

$2v$

Question 25: Palette 25/112

Objective 2014 MCQ

A car moves from $ A $ to $ B $ with a speed of $ 30\mathrm{kmh}^{-1} $ and from $ B $ to $ A $ with a speed of $ 20\mathrm{kmh}^{-1} $. What is the average speed of the car? (KCET 2014)

A

$25\mathrm{kmh}^{-1}$

B

$24\mathrm{kmh}^{-1}$

C

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

D

$10\mathrm{kmh}^{-1}$

Question 26: Palette 26/112

Objective 2014 MCQ

A body starts from rest and moves with constant acceleration for t second. It travels a distance $ x_{1} $ in first half of time and $ x_{2} $ in next half of time, then (KCET 2014)

A

$x_{2} = x_{1}$

B

$x_{2} = 2x_{1}$

C

$x_{2} = 3x_{1}$

D

$x_{2} = 4x_{1}$

Question 27: Palette 27/112

Objective Kerala CEE 2014 MCQ

The acceleration of a moving body is found from the

A

area under velocity-time graph

B

area under displacement-time graph

C

slope of distance-time graph

D

slope of velocity-time graph

E

None of the above

Question 28: Palette 28/112

Objective NEET 2013 MCQ

A stone falls freely under gravity. It covers distances $ h_{1} $ , $ h_{2} $ and $ h_{3} $ in the first 5 s, the next 5 s and the next 5 s, respectively. The relation between $ h_1 $, $ h_2 $ and $ h_3 $ is

A

$h_1 = 2h_2 = 3h_3$

B

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

C

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

D

$h_1 = h_2 = h_3$

Question 29: Palette 29/112

Objective J&K CET 2013 MCQ

The motion of a particle in straight line is an example of

A

constant velocity motion

B

uniformly accelerated motion

C

non-uniformly accelerated motion

D

zero velocity motion

Question 30: Palette 30/112

Objective J&K CET 2013 MCQ

The velocity-time graph of particle comes out to be a non-linear curve. The motion is

A

uniform velocity motion

B

uniformly accelerated motion

C

non-uniform accelerated motion

D

Nothing can be said about the motion

Question 31: Palette 31/112

Objective EAMCET 2013 MCQ

A body is thrown vertically upward from a point A 125 m above the ground. It goes up to a maximum height of 250 m above the ground and passes through A on its downward journey. The velocity of the body when it is at a height of 70 m above the ground is (Take, g = 10 ms $ ^{-2} $ )

A

50 ms $ ^{-1} $

B

60 ms $ ^{-1} $

C

80 ms $ ^{-1} $

D

20 ms $ ^{-1} $

Question 32: Palette 32/112

Objective EAMET 2013 MCQ

A person reaches a point directly opposite on the other bank of a river. The velocity of the water in the river is $ 4 \, ms^{-1} $ and the velocity of the person in still water is $ 5 \, ms^{-1} $ . If the width of the river is 84.6 m, time taken to cross the river (in seconds) is

A

28.2

B

9.4

C

2

D

84.6

Question 33: Palette 33/112

Objective UP CPMT 2013 MCQ

The velocity-time graph of robber's car and a chasing police car are shown in the following graph. Police car crosses the robber's car in time

A

10 s after it starts

B

15 s after it starts

C

20 s after it starts

D

Never crosses

Question 34: Palette 34/112

Objective BCCEE 2013 MCQ

Initial speed of an $\alpha$ -particle inside a tube of length $4\mathrm{m}$ is $1\mathrm{kms}^{-1}$ , if it is accelerated in the tube and comes out with a speed of $9\mathrm{kms}^{-1}$ , then the time for which the particle remains inside the tube is

A

$8 \times 10^{-3} \mathrm{~s}$

B

$8 \times 10^{-4} \mathrm{~s}$

C

$80 \times 10^{-3} \mathrm{~s}$

D

$800 \times 10^{-3} \mathrm{~s}$

Question 35: Palette 35/112

Objective CBSE AIMPT 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

$24 \mathrm{~ms}^{-2}$

B

zero

C

$6\mathrm{ms}^{-2}$

D

$12\mathrm{ms}^{-2}$

Question 36: Palette 36/112

Objective AIIMS 2012 MCQ

A particle moves along with X-axis. The position x of particle with respect to time t from origin given by $ x = b_{0} + b_{1}t + b_{2}t^{2} $ . The acceleration of particle is

A

$b_{0}$

B

$b_{1}$

C

$b_{2}$

D

$2b_{2}$

Question 37: Palette 37/112

Objective BCECE 2012 MCQ

A body X is projected upwards with a velocity of $ 98 \, ms^{-1} $ , after 4 s, a second body Y is also projected upwards with the same initial velocity. Two bodies will meet after

A

8 s

B

10 s

C

12 s

D

14 s

Question 38: Palette 38/112

Objective BHU 2012 MCQ

A scooter starts from rest have an acceleration of $1\mathrm{ms}^{-2}$ while a car $150\mathrm{m}$ behind it starts from rest with an acceleration of $2\mathrm{ms}^{-2}$. After how much time, the car catches up with the scooter?

A

$\sqrt{700}$ s

B

$\sqrt{300}$ s

C

$\sqrt{150}$ s

D

None of these

Question 39: Palette 39/112

Objective AMU 2012 MCQ

Let $\mathbf{r}_1(t) = 3t\mathbf{i} + 4t^2\mathbf{j}$ and $\mathbf{r}_2(t) = 4t^2\mathbf{i} + 3\mathbf{j}$ represent the positions of particles 1 and 2, respectively, as function of time t, $\mathbf{r}_1(t)$ and $\mathbf{r}_2(t)$ are in metre and t in second. The relative speed of the two particles at the instant $t = 1\mathrm{s}$, will be

A

$1\mathrm{m / s}$

B

$3\sqrt{2}\mathrm{m / s}$

C

$5\sqrt{2}\mathrm{m / s}$

D

$7\sqrt{2}\mathrm{m / s}$

Question 40: Palette 40/112

Objective MCQ

A boy walks to his school at a distance of 6 km with constant speed of $ 2.5 \, km h^{-1} $ and walks back with a constant speed of $ 4 \, km h^{-1} $ . His average speed for round trip expressed (in $ km h^{-1} $ ), is

A

24/13

B

40/13

C

3

D

1/2

Question 41: Palette 41/112

Objective 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

6 m

D

4 m

Question 42: Palette 42/112

Objective MCQ

A vehicle travels half the distance $ l $ with speed $ v_{1} $ and the other half with speed $ v_{2} $, then its average speed is [NCERT Exemplar]

A

$ \frac{v_1 + v_2}{2} $

B

$ \frac{2v_1 + v_2}{v_1 + v_2} $

C

$ \frac{2v_1v_2}{v_1 + v_2} $

D

$ \frac{l(v_1 + v_2)}{v_1v_2} $

Question 43: Palette 43/112

Objective MCQ

Which of the following speed-time $(v - t)$ graphs is physically not possible?

A

B

C

D

All of these

Question 44: Palette 44/112

Objective 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 (in second) is

A

12

B

9

C

10

D

1.8

Question 45: Palette 45/112

Objective MCQ

A man walks on a straight road from his home to a market 2.5 km away with a speed of $ 5 \, kmh^{-1} $ . Finding the market closed, he instantly turns and walks back home with a speed of $ 7.5 \, kmh^{-1} $ . The average speed of the man over the interval of time 0 to 50 min is equal to

A

$ 5 \, kmh^{-1} $

B

$\frac{25}{4}\mathrm{kmh}^{-1}$

C

$\frac{30}{5}\mathrm{kmh}^{-1}$

D

$\frac{45}{8}\mathrm{kmh}^{-1}$

Question 46: Palette 46/112

Objective MCQ

A car moving with a velocity of $ 10 \, ms^{-1} $ can be stopped by the application of a constant force F in a distance of 20 m. If the velocity of the car is $ 30 \, ms^{-1} $ , it can be stopped by this force in

A

$\frac{20}{3}\mathrm{m}$

B

20 m

C

60 m

D

180 m

Question 47: Palette 47/112

Objective 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 distance in the 5th second, after the start of A, the then ratio $ a_{1}:a_{2} $ is equal to

A

5:9

B

5:7

C

9:5

D

9:7

Question 48: Palette 48/112

Objective MCQ

The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point

A

E

B

F

C

C

D

D

Question 49: Palette 49/112

Objective MCQ

Figure given shows the distance-time graph of the motion of a car. It follows from the graph that the car is

A

at rest

B

in uniform motion

C

in non-uniform accelerated motion

D

uniformly accelerated motion

Question 50: Palette 50/112

Objective MCQ

The velocity of a body depends on time according to the equation $ v = \frac{t^{2}}{10} + 20 $ . The body is undergoing

A

uniform acceleration

B

uniform retardation

C

non-uniform acceleration

D

zero acceleration

Question 51: Palette 51/112

Objective MCQ

The velocity v of a particle as a function of its position (x) is expressed as $ v = \sqrt{c_{1} - c_{2}x} $ , where $ c_{1} $ and $ c_{2} $ are positive constants. The acceleration of the particle is

A

$c_{2}$

B

$-\frac{c_2}{2}$

C

$c_{1} - c_{2}$

D

$\frac{c_1 + c_2}{2}$

Question 52: Palette 52/112

Objective MCQ

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

A

27 s

B

50 s

C

18 s

D

36 s

Question 53: Palette 53/112

Objective MCQ

Particle A is moving along X-axis. At time t = 0, it has velocity of $ 10 \, ms^{-1} $ and acceleration $ -4 \, ms^{-2} $ . Particle B has velocity of $ 20 \, ms^{-1} $ and acceleration $ -2 \, ms^{-2} $ . Initially both the particles are at origin. At time t = 2 s, distance between the two particles is

A

24 m

B

36 m

C

20 m

D

42 m

Question 54: Palette 54/112

Objective 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 55: Palette 55/112

Objective MCQ

A car starts moving along a line, first with acceleration $ a = 5 \, ms^{-2} $ starting from rest, then uniformly and finally decelerating at the same rate a and comes to rest. The total time of motion is $ 25 \, s $ . The average speed during the time is $ 20 \, ms^{-1} $ . How long does particle move uniformly?

A

10 s

B

12 s

C

20 s

D

15 s

Question 56: Palette 56/112

Objective 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 QQ 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

0,214

Question 57: Palette 57/112

Objective MCQ

A body starts from rest with uniform acceleration a. The acceleration of the body as function of time t is given by the equation $ a = pt $ , where p is a constant, then the displacement of the particle in the time interval t = 0 to $ t = t_{1} $ will be

A

$\frac{1}{2} pt_1^2$

B

$\frac{1}{3} pt_1^2$

C

$\frac{1}{2} pt_1^2$

D

$\frac{1}{6} pt_1^3$

Question 58: Palette 58/112

Objective MCQ

A particle moves along a straight line OX. At a time t (in seconds), the distance $ 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 59: Palette 59/112

Objective 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 60: Palette 60/112

Objective MCQ

The ratios of the distance traversed, in successive intervals of time by a body, falling from rest, are

A

1:3:5:7:9:...

B

2:4:6:8:10:...

C

1:4:7:10:13:...

D

None of these

Question 61: Palette 61/112

Objective MCQ

A particle starts from rest. Its acceleration (a) versus time (t) graph 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 62: Palette 62/112

Objective MCQ

A ball is dropped onto the floor from a height of 10 m. It rebounds to a height of 5 m. If the ball was in contact with the floor for 0.01 s, what was its average acceleration during contact? (Take, $ g = 10 \, ms^{-2} $ )

A

$2414\mathrm{ms}^{-2}$

B

$1735\mathrm{ms}^{-2}$

C

$ 3120 \, ms^{-2} $

D

$4105\mathrm{ms}^{-2}$

Question 63: Palette 63/112

Objective 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 64: Palette 64/112

Objective MCQ

A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. Then, which amongst the following option is correct about the relation between the distance covered by the boggy and distance covered by the train in the same time?

A

Both will be equal

B

First will be half of second

C

First will be 1/4 of second

D

No definite ratio

Question 65: Palette 65/112

Objective 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 is

A

3 s

B

4.5 s

C

5 s

D

6 s

Question 66: Palette 66/112

Objective MCQ

The displacement $ x $ of a particle varies with time $ t $ as $ x = ae^{-at} + 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 67: Palette 67/112

Objective MCQ

A stone is allowed to fall freely from rest. The ratio of the time taken to fall through the first metre and the second metre distance is

A

$\sqrt{2} - 1$

B

$\sqrt{2} + 1$

C

$\sqrt{2}$

D

None of these

Question 68: Palette 68/112

Objective MCQ

Amongst the following equation of motion, which represents uniformly accelerated motion?

A

$x = \sqrt{\frac{t + \alpha}{b}}$

B

$x = \frac{t + \alpha}{b}$

C

$t = \sqrt{\frac{x + a}{b}}$

D

$x = \sqrt{t + a}$

Question 69: Palette 69/112

Objective MCQ

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

A

$20\mathrm{m}$

B

$18\mathrm{m}$

C

$16\mathrm{m}$

D

$25\mathrm{m}$

Question 70: Palette 70/112

Objective 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) $ ^{3/2} $

B

(distance) $ ^{2} $

C

(distance) $ ^{-2} $

D

(velocity) $ ^{2/3} $

Question 71: Palette 71/112

Objective MCQ

A particle moves along a straight line. Its position at any instant is given by $ x = 32t - \frac{8t^3}{4} $, where $ x $ is in metre and $ t $ is in second. Find the acceleration of the particle at the instant when particle is at rest.

A

$-16\mathrm{ms}^{-2}$

B

$-27.6\mathrm{ms}^{-2}$

C

$32\mathrm{ms}^{-2}$

D

$16\mathrm{ms}^{-2}$

Question 72: Palette 72/112

Objective MCQ

Two particles $ P $ and $ Q $ simultaneously start moving from point $ A $ with velocities $ 15\mathrm{ms}^{-1} $ and $ 20\mathrm{ms}^{-1} $ respectively. The two particles move with accelerations equal in magnitude but opposite in direction. When $ P $ overtakes $ Q $ at $ B $, then its velocity is $ 30\mathrm{ms}^{-1} $. The velocity of $ Q $ at point $ B $ will be

A

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

B

$5\mathrm{ms}^{-1}$

C

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

D

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

Question 73: Palette 73/112

Objective MCQ

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

A

$12\mathrm{ms}^{-1}$

B

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

C

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

D

$16\mathrm{ms}^{-1}$

Question 74: Palette 74/112

Objective MCQ

A point moves in a straight line, so that its displacement $ x $ at time $ t $ is given by $ x^2 = t^2 + 1 $. Its acceleration is

A

$1 / x$

B

$1 / x^{3}$

C

$-1 / x^{2}$

D

$-1 / x^{3}$

Question 75: Palette 75/112

Objective MCQ

A point moves with uniform acceleration and $ v_{1}, v_{2} $ and $ v_{3} $ denote the average velocities in the three successive intervals of time $ t_1, t_2 $ and $ t_3 $. Which of the following relations is correct?

A

$(v_{1} - v_{2}):(v_{2} - v_{3}) = (t_{1} - t_{2}):(t_{2} + t_{3})$

B

$(v_{1} - v_{2}):(v_{2} - v_{3}) = (t_{1} + t_{2}):(t_{2} + t_{3})$

C

$(v_{1} - v_{2}):(v_{2} - v_{3}) = (t_{1} - t_{2}): (t_{1} - t_{3})$

D

$(v_{1} - v_{2}):(v_{2} - v_{3}) = (t_{1} - t_{2}):t_{2} - t_{3})$

Question 76: Palette 76/112

Objective MCQ

The velocity-time graph for a particle moving along X-axis is shown in the figure. The corresponding displacement-time graph is correctly shown by

A

B

C

D

Question 77: Palette 77/112

Objective MCQ

The vertical height of point $ P $ above the ground is twice that of $ Q $. A particle is projected downward with a speed of $ 5\mathrm{ms}^{-1} $ from $ P $ and at the same time, another particle is projected upward with the same speed from $Q$. Both particles reach the ground simultaneously, then

A

PQ = 30 m

B

time of flight of stones = 3 s

C

Both

D

Both

Question 78: Palette 78/112

Objective 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 metre is (Take, g = 10 ms $ ^{-2} $ )

A

60

B

45

C

80

D

50

Question 79: Palette 79/112

Objective MCQ

The acceleration-time $(a - t)$ graph for a particle moving along a straight line starting from rest is shown in figure. Which of the following graph is the best representation of variation of its velocity $(v)$ with time $(t)$?

A

B

C

D

Question 80: Palette 80/112

Objective MCQ

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

A

a

B

b

C

c

D

d

Question 81: Palette 81/112

Objective MCQ

The displacement $ x $ of a particle in a straight line motion is given by $ x = 1 - t - t^2 $. The correct representation of the motion is

A

B

C

D

Question 82: Palette 82/112

Objective MCQ

Among the four graph shown in the figure, there is only one graph for which average velocity over the time interval $ (0, T) $ can vanish for a suitably chosen T. Which one is it? [NCERT Exemplar]

A

B

C

D

Question 83: Palette 83/112

Objective MCQ

A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct? [NCERT Exemplar]

A

$x < 0, v < 0, a > 0$

B

$x > 0, v < 0, a < 0$

C

$x > 0, v < 0, a > 0$

D

$x > 0, v > 0, a < 0$

Question 84: Palette 84/112

Objective MCQ

The displacement of a particle is given by $x = (t - 2)^{2}$, where $x$ is in metre and $t$ in second. The distance covered by the particle in first 4 seconds is [NCERT Exemplar]

A

$4\mathrm{m}$

B

$8\mathrm{m}$

C

$12\mathrm{m}$

D

$16\mathrm{m}$

Question 85: Palette 85/112

Objective 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

$50\mathrm{m}$

B

$75\mathrm{m}$

C

$100\mathrm{m}$

D

$125\mathrm{m}$

Question 86: Palette 86/112

Objective MCQ

A particle moving along $X$-axis has acceleration $f$, at time $t$, given $f = f_0\left(1 - \frac{t}{T}\right)$, where $f_0$ and $T$ are constants. The particle at $ t = 0 $ has zero velocity. When $ f = 0 $, the particle's velocity $ (v_{x}) $ is

A

$\frac{1}{2} f_0T$

B

$f_{0}T$

C

$\frac{1}{2} f_0T^2$

D

$f_0T^{-2}$

Question 87: Palette 87/112

Objective MCQ

An elevator car whose floor to ceiling distance is 2.7m starts ascending with a constant acceleration of $ 1.2 \, ms^{-2} $ . 2 s after the start, a bolt falls from the ceiling of the car. The free fall time of the bolt is (Take, $ g = 9.8 \, ms^{-2} $ )

A

$\sqrt{\frac{2.7}{9.8}}\mathrm{s}$

B

$\sqrt{\frac{5.4}{9.8}}\mathrm{s}$

C

$\sqrt{\frac{5.4}{8.6}}\mathrm{s}$

D

$\sqrt{\frac{5.4}{11}}\mathrm{s}$

Question 88: Palette 88/112

Objective MCQ

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

A

293 m

B

11 1m

C

91 m

D

182 m

Question 89: Palette 89/112

Objective MCQ

Two cars A and B are travelling in the same direction with velocities $ v_{1} $ and $ v_{2}(v_{1} > v_{2}) $ . When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when

A

$d < \frac{(v_1 - v_2)^2}{2a}$

B

$d < \frac{v_1^2 - v_2^2}{2a}$

C

$d > \frac{(v_1 - v_2)^2}{2a}$

D

$d > \frac{v_1^2 - v_2^2}{2a}$

Question 90: Palette 90/112

Objective MCQ

Water drops fall at regular intervals from a tap which is 5 m above the ground. The third drop is leaving the tap at the instant, the first drop touches the ground. How far above the ground is the second drop at that instant?

A

$2.50\mathrm{m}$

B

$3.75\mathrm{m}$

C

$4.00\mathrm{m}$

D

$1.25\mathrm{m}$

Question 91: Palette 91/112

Objective 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 92: Palette 92/112

Objective MCQ

A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d / 2$. Neglecting subsequent motion and air resistance, its velocity $v$ varies with the height $h$ above the ground can be plotted as

A

B

C

D

Question 93: Palette 93/112

Objective 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 positive $ x $-direction?

A

24 m

B

32 m

C

54 m

D

81 m

Question 94: Palette 94/112

Objective MCQ

A car A moves along north with velocity 30 km/h and another car B moves along east with velocity 40 km/h. The relative velocity of A with respect to B is

A

50 km/h north-east

B

50 km/h north-west

C

50 km/h at angle $\tan^{-1}(3/4)$ north of west

D

50 km/h at angle $\tan^{-1}(4/3)$ west of north

Question 95: Palette 95/112

Objective MCQ

Rain is falling vertically downward with velocity 4 m/s. A man is moving horizontally with velocity 3 m/s, the velocity of rain with respect to man is

A

5 m/s at an angle $\tan^{-1}(4/3)$ with horizontal

B

5 m/s at an angle $\tan^{-1}(3/4)$ with vertical

C

5 m/s at an angle $\tan^{-1}(4/3)$ with vertical

D

Both

Question 96: Palette 96/112

Objective MCQ

A ship is travelling due east at a speed of 15 km/h. Find the speed of a boat heading $ 30^{\circ} $ east of north, if it always appears due north from the ship.

A

$30\mathrm{km / h}$

B

$\frac{15\sqrt{3}}{2}\mathrm{km / h}$

C

$10\sqrt{3}\mathrm{km / h}$

D

$20\mathrm{km / h}$

Question 97: Palette 97/112

Objective MCQ

A man takes 3 h to cover a certain distance along the flow of river and takes 6 h to cover the same distance opposite to the flow of river. In how much time, he will cross this distance in still water?

A

$3.5\mathrm{h}$

B

4 h

C

$4.5\mathrm{h}$

D

$5\mathrm{h}$

Question 98: Palette 98/112

Objective MCQ

A river 500 m wide is flowing at a rate of 4 m/s. A boat is sailing at a velocity of 10 m/s with respect to the water in a direction perpendicular to the river. The time taken by the boat to reach the opposite bank is

A

30 s

B

40 s

C

50 s

D

60 s

Question 99: Palette 99/112

Objective MCQ

Assertion: A body is momentarily at rest at the instant, it reverses the direction. Reason: A body cannot have acceleration, if its velocity is zero at a given instant of time.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 100: Palette 100/112

Objective MCQ

Assertion: The $ v - t $ graph perpendicular to time axis is not possible in practice. Reason: Infinite acceleration cannot be realised in practice.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 101: Palette 101/112

Objective MCQ

Assertion: In the $s - t$ diagram as shown in figure, the body starts moving in positive direction but not from s = 0. Reason: At $ t = t_0 $, velocity of body changes its direction of motion.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 102: Palette 102/112

Objective MCQ

Assertion: If acceleration of a particle moving in a straight line varies as $ a \propto t^{n} $ , then $ s \propto t^{n+2} $ . Reason: If $ a \cdot t $ graph is a straight line, then $ s \cdot t $ graph may be a parabola.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 103: Palette 103/112

Objective MCQ

Assertion: A lift is ascending with decreasing speed means acceleration of lift is downwards. Reason: A body always moves in the direction of its acceleration.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is correct but Reason is incorrect.

D

If Assertion is incorrect but Reason is correct.

Question 104: Palette 104/112

Objective MCQ

The displacement (x)-time (t) graph of a particle is shown in figure. Then, which of the following statement is correct?

A

Particle starts with zero velocity and variable acceleration.

B

Particle starts with non-zero velocity and variable acceleration.

C

Particle starts with zero velocity and uniform acceleration.

D

Particle starts with non-zero velocity and uniform acceleration.

Question 105: Palette 105/112

Objective MCQ

A particle moves along $X$-axis as $x = 4 (t - 2) + a (t - 2) ^ {2}$ Which of the following statement is true?

A

The initial velocity of particle is 4.

B

The acceleration of particle is 2a.

C

The particle is at origin at $ t = 0 $.

D

None of the above

Question 106: Palette 106/112

Objective MCQ

In one dimensional motion, instantaneous speed $ v $ satisfies $ 0 \leq v < v_0 $. Then, which of the following statement is true? [NCERT Exemplar]

A

The displacement in time $ T $ must always take non-negative values.

B

The displacement $ x $ in time $ T $ satisfies
$$<br /> v - v _ {0} T < x < v _ {0} T.<br /> $$

C

The acceleration is always a non-negative number.

D

The motion has no turning points.

Question 107: Palette 107/112

Objective MCQ

I. If a particle is thrown upwards, then distance travelled in last second of upward journey is independent of the velocity of projection. II. In last second, distance travelled is 4.9 m. (Take, g = 9.8 ms $ ^{-2} $ ) Which amongst the statement(s) is/are correct?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Question 108: Palette 108/112

Objective MCQ

I. In the $ \nu-t $ diagram as shown in figure, average velocity between the interval t = 0 and $ t = t_{0} $ is independent of $ t_{0} $ . II. Average velocity in the given interval is $\frac{1}{2}\nu_{m}$. Which amongst the statement(s) is/are correct?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Question 109: Palette 109/112

Objective 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 (Take, g = 10 m/s $ ^{2} $ )

A

340 m

B

320 m

C

300 m

D

360 m

Question 110: Palette 110/112

Objective MCQ

The speed of a swimmer in still water is 20 ms $ ^{-1} $ . The speed of river water is 10 ms $ ^{-1} $ 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

$0^{\circ}$

B

$60^{\circ}$, west

C

$45^{\circ}$, west

D

$30^{\circ}$, west

Question 111: Palette 111/112

Objective MCQ

A runner starts from O and goes to O following path OQRO in 1 h. What is net displacement and average speed?

A

0, 3.57 kmh $ ^{-1} $

B

0, 0 kmh $ ^{-1} $

C

0, 2.57 kmh $ ^{-1} $

D

0, 1 kmh $ ^{-1} $

Question 112: Palette 112/112

Objective MCQ

What will be the a versus x graph for the following graph?

A

A

B

B

C

C

D

D