Rankers JEE

Graph (kinematics) XITH D.P.P. # 2

1. The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and
Q respectively are shown in the graph. Choose the correct entry below

(1) B lives closer to school than A

(2) B starts from the school earlier than A
(3) A walks faster than B
(4) B overtakes A on the road
2. Look at the graphs carefully, and mark which of these can represent one-dimensional motion
(1) a (2) b (3) c (4) d

3. Figure gives the x-t plot of a particle executing one dimension simple harmonic motion. Mark the correct
combination. The signs of position, velocity and acceleration variables at

(1) t = 0.3 s, x < 0, v < 0, a < 0

(2) t = 1.2 s, x > 0, v > 0, a > 0
(3) t = -1.2 s, x > 0, v > 0, a < 0
(4) t = -0.3 s, x > 0, v < 0, a < 0

4. Figure gives the x-t plot of a particle in one-dimensional motion. Three different equal intervals of time are
shown. Let v1,v2,v3 be the average speed in each of the intervals respectively, then
(1) v1 < v2 > v3
(2) v2 > v1 > v3
(3) v3 > v1 > v2
(4) v2 > v1 < v3

5. Figure gives speed time graph of a particle in motion along a constant direction. Three equal intervals of
time are shown. Mark the incorrect statement.
Among the three intervals,
(1) The average acceleration in the second interval is greatest
(2) The average speed is greatest in the third interval
(3) The acceleration at A,B,C,D is zero
(4) The distance travelled in the second interval is greatest

6. Two stones are thrown up simultaneously from the edge of a cliff 200 m high with initial speeds of 15 ms-
1
and 30 ms-1. Taking g = 10 ms-2, the graph of relative positive of the second stone with respect to the
first has been shown. The equation of the curved part is

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(1) 100 + 15t – t2
(2) 200 + 30t – 5t2
(3) 200 – 15t + 5t2
(4) 100 – 30t + 5t2
7. The speed time graph of a particle moving along a fixed direction is shown. The distance traversed by the
particle in
(1) 20m
(2) 30m
(3) 40 m
(4) 60
8. The graph shown in figure shows the velocity v versus time t for a body. Which of the graphs shown in
figure represent the corresponding acceleration versus time graph ?

9. The graph depicts the velocity of an object at various times during its motion. The shaded portion of the
graph has an area equal to
(1) the average acceleration
(2) distance moved during uniform motion
(3) distance moved during accelerated motion
(4) the average velocity
10. Which of the following curves represents the v-t graph of an object falling on a metallic surface and
bouncing back ?

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11. The variation of velocity of a particle moving along a straight line is shown in the figure. The distance
travelled by the particle in 4 s is
(1) 25 m
(2) 30 m
(3) 55 m
(4) 60 m
12. Figure show the displacement-time graphs of two particles moving along the x-axis. We can say that

(1) Both the particles are having a uniformly retarded motion.

(2) Both the particles are having a uniformly accelerated motion
(3) Particle (i) is having a uniformly accelerated motion
While particle (ii) is having a uniformly retarded motion
(4) Particle (i) is having a uniformly retarded motion while particle (ii) is having a uniformly accelerated
motion.
13. A rocket is fired upwards. Its engine explodes fully in 12 seconds. The height reached by the rocket as
calculated from its velocity-time graph is

(1) 1200 × 66 m
(2) 1200 × 132 m
1200
(3) 𝑚
12
(4) 1200 × 122 m
14. A ball is projected vertically upwards. Which graph in the figure represents the velocity of the ball during
its flight when air resistance is ignored ?

(2) B (3) C (4

15. In the velocity-time graph shown in the figure, the distance travelled by the particle between 1.0 second
and 4.0 second is nearly

(1) 39 m
(2) 60 m
(3) 80 m
(4) 100 m

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16. The following figures show velocity v versus time t curves. But only some of these can be realised in
practice. These are

(1) (i),(ii) and (iv) only

(2) (i),(ii) and (iii) only

(3) (i) and (iv) only

(4) all

17. A particle starts from rest at time t = 0 and moves on a straight line with acceleration as plotted in figure.
The speed of the particle will be maximum after time

(1) 1 s
(2) 2 s
(3) 3 s
(4) 4 s
18. The velocity versus time graphs of a moving particle is shown in figure. The maximum acceleration is

(1) 1 ms-2
(2) 2 ms-2

(3) 3 ms-2
(4) 4 ms-2

19. Which one of the following represents the time-displacement graph of two objects P and Q moving with
zero relative speed ?

20. In the displacement d versus time t graph given below the value of average
velocity in the time interval 0 to 20 s is (in m/s).

(1) 1.5 (2) 4

(3) 1 (4) 2

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21. Four velocity-time graphs (namely I,II,III and IV) are shown in figure. In which case is the acceleration
uniform and position ?

(1) I
(2) II
(3) III
(4) IV

22. Figure shows the position of a particle moving along the x-axis as a function of time.
(1) The particle has come to rest 6 times

(2) The maximum speed is at t = 6 s

(3) The velocity remains positive for t = 0 to t = 6 s.

(4) The average velocity for the total period shown is negative
23. The displacement-time graphs of two moving particles make angles of 300 and 450 with the x-axis. The
ratio of the two velocities is

(1) 3 ∶ 1
(2) 1 : 1

(3) 1 : 2
(4) 1 : 3

24. Which of the following represents uniform speed ?

25. Figures shows the graphical variation of displacement with time for
the case of a particle moving along a straight line. The accelerations
of the particle during the intervals OA,AB,BC and CD are respectively.

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26. From a high tower at time t = 0, one stone is dropped from rest and simultaneously another stone is
projected vertically up with an initial velocity. The graph of the distance ‘s’ between the two stones, before
either hits the ground, plotted against time ‘t’ will be as

27. A graph of acceleration versus time of a particle starting from rest at t = 0 is as shown in figure. The speed
of the particle at t = 14 second is

(1) 2 ms-1
(2) 34 ms-1
(3) 20 ms-1
(4) 42 ms-1

28. The velocity-time graph of a moving train is depicted in figure. The average velocity in time OD is

(1) 30 ms-1

(2) 60 ms-1

(3) 45 ms-1
(4) 23 ms-1

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

(1) C
(2) D
(3) E
(4) F

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30. In the given v-t graph, the distance travelled by the body in 5 second will be

(1) 20 m
(2) 40 m
(3) 80 m
(4) 100 m

31. The velocity-time graph of a particle in linear motion is shown in figure. Both v and t are in SI units. What
is the displacement of the particle from the origin after 8 second ?

(1) 6m
(2) 8 m
(3) 16 m
(4) 18 m
32. Which of the following graphs represents the distance-time variation of a body released from the top of a
building ?

33. The speed versus time graph of a body is shown in figure. Which of the following statement is correct ?
(1) the body is moving with uniform acceleration of 6.67 ms-2 at all the times

(2) the body is at rest for 1 s and has a uniform acceleration of 6.67 ms-2

(3) the body is at rest for one second and has a uniform acceleration of 5 ms-2
afterwards

(4) the body is at rest for 1 s and has a uniform retardation of 6.67 ms-2 afterwards
34. A particle moves along X-axis in such a way that its x-coordinate varies with time t according to the
equation x = (6 – 4t + 6t2) metre. The velocity of the particle will vary with time according to the graph

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35. The displacements of a particle as a function of time t is shown in figure. The figure indicates

(1) the velocity of the particle is constant throughout

(2) the particle starts with certain velocity, but the motion is retarded
and finally the particle stops
(3) the particle starts with a constant velocity, the motion is accelerated
and finally the particle moves with another constant velocity.
(4) The acceleration of the particle is constant throughout.

36. A particle starts from rest and moves along a straight line with constant acceleration. The variation of
velocity v with displacement s is

37. Which of the graphs below correctly shows how the acceleration and velocity of a perfectly elastic ball
bouncing on a horizontal surface varying with time?

38. Figure shows the time-displacement graph of the particles A and B. Which of the following
statements is correct ?

(1) Both A and B move with uniform equal speed.

(2) A is accelerated, B is retarded.
(3) Both A and B move with uniform speed. The speed of B is more than the speed of A
(4) Both A and B move with uniform speeds but the speed of A is more than the speed of B.

39. A football is rolling down a hill of unknown shape. The speed of the football at different times is notes as
given below.

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Time Instantaneous speed
0s 0 ms-1
1s 4 ms-1
2s 8 ms-1
3s 12 ms-1
4s 16 ms-1
The correct shape of the hill is depicted in

40. For the displacement-time graph shown in figure the ratio of the magnitudes of the speeds during the first
two seconds and the next four second is

(1) 1 : 1
(2) 2 : 1
(3) 1 : 2
(4) 3 : 2

41. Which of the following represents an impossible situation ?

42. What does the shaded portion in figure represent ?

(1) momentum
(2) acceleration
(3) distance
(4) velocity

43. Figure give the time (t) versus velocity (v) relation for a vehicle moving in a straight path. The
displacement between t = 0 and t = 12.5 s is
(1) 30 m (2) 150 m
(3) 75 m (4) 125 m

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