Quiz - physics - Motion in a Straight Line-PYQ

Q1. A particle covers half of its total distance with speed \( v_1 \) and the rest half distance with speed \( v_2 \). Its average speed during the complete journey is Source: orcusprep.in

AIPMT Mains 2011

easy

\( \frac{v_1+v_2}{2} \)

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

\( \frac{2v_1v_2}{v_1+v_2} \)

\( \frac{v_1^2+v_2^2}{v_1+v_2} \)

Q2. A car 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 Source: orcusprep.in

AIPMT 2007

easy

\( v_d v_u \)

\( \frac{v_d + v_u}{v_d v_u} \)

\( \frac{v_u + v_d}{2} \)

\( \frac{2v_d v_u}{v_d + v_u} \)

Q3. A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is Source: orcusprep.in

AIPMT 2006

easy

10 m/s, 0

0, 0

0, 10 m/s

10 m/s, 10 m/s.

Q4. A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and the second half of distance at speed v. The average speed is 48 km/h. The value of v is Source: orcusprep.in

AIPMT 1991

medium

56 km/h

60 km/h

50 km/h

48 km/h.

Q5. A bus travelling the first one-third distance at a speed of 10 km/h, the next one-third at 20 km/h and at last one-third at 60 km/h. The average speed of the bus is Source: orcusprep.in

AIPMT 1991

medium

9 km/h

16 km/h

18 km/h

48 km/h.

Q6. A car covers the first half of the distance between two places at 40 km/h and another half at 60 km/h. The average speed of the car is Source: orcusprep.in

AIPMT 1990

easy

40 km/h

48 km/h

50 km/h

60 km/h.

Q7. Two cars P and Q start from a point at the same time in a straight line and their positions are represented by \( x_P(t) = at + bt^2 \) and \( x_Q(t) = ft - t^2 \). At what time do the cars have the same velocity? Source: orcusprep.in

NEET-II 2016

medium

\( \frac{a - f}{1+b} \)

\( \frac{a-f}{2(1-b)} \)

\( \frac{a+f}{2(1+b)} \)

\( \frac{f - a}{2(1+b)} \)

Q8. If the velocity of a particle is \( v = At + Bt^2 \), where A and B are constants, then the distance travelled by it between 1 s and 2 s is Source: orcusprep.in

NEET-I 2016

medium

\( \frac{3}{2}A + \frac{7}{3}B \)

\( \frac{A}{2} + \frac{B}{3} \)

\( \frac{3}{2}A + 4B \)

\( 3A + 7B \)

Q9. The displacement ‘x’ (in meter) of a particle of mass ‘m’ (in kg) moving in one dimension under the action of a force, is related to time ‘t’ (in sec) by \( t = \sqrt{x} + 3 \). The displacement of the particle when its velocity is zero, will be Source: orcusprep.in

Karnataka NEET 2013

medium

4 m

0 m (zero)

6 m

2 m

Q10. A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point Source: orcusprep.in

AIPMT 2008

easy

D

A

B

C

Q11. 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 seconds. What will be the position of this particle when it achieves maximum speed along the +x direction? Source: orcusprep.in

AIPMT 2007

medium

54 m

81 m

24 m

32 m.

Q12. 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? Source: orcusprep.in

AIPMT 2006

medium

16 m

24 m

40 m

56 m

Q13. The displacement x of a particle varies with time t as \( x = ae^{-at} + be^{bt} \), where a, b, \( \alpha \) and \( \beta \) are positive constants. The velocity of the particle will Source: orcusprep.in

AIPMT 2005

easy

be independent of \( \beta \)

drop to zero when \( \alpha = \beta \)

go on decreasing with time

go on increasing with time.

Q14. The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point Source: orcusprep.in

AIPMT 1994

easy

E

F

C

D

Q15. 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 particle as a function of x, is given by Source: orcusprep.in

NEET 2015 Cancelled

medium

\( -2b^2x^{-2n + 1} \)

\( -2nb^2e^{-4n + 1} \)

\( -2nb^2x^{-2n - 1} \)

\( -2nb^2x^{-4n - 1} \)

Q16. The motion of a particle along a straight line is described by equation \( x = 8 + 12t^2 - t^3 \) where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is Source: orcusprep.in

AIPMT 2012

medium

24 m/s^2

zero

6 m/s^2

12 m/s^2

Q17. A particle moves a distance x in time t according to equation \( x = (t + 5)^{-1} \). The acceleration of particle is proportional to Source: orcusprep.in

AIPMT 2010

medium

(velocity)\(^{3/2}\)

(distance)\(^{2}\)

(distance)\(^{-2}\)

(velocity)\(^{2/3}\)

Q18. A particle moving along x-axis has acceleration f, at time t, given by \( f = f_0(1 - \frac{t}{T}) \), where \( f_0 \) and T are constants. The particle at \( t = 0 \) has zero velocity. In the time interval between \( t = 0 \) and the instant when \( f = 0 \), the particle’s velocity (\( v_x \)) is Source: orcusprep.in

AIPMT 2007

medium

\( \frac{1}{2} f_0T^2 \)

\( f_0T^2 \)

\( \frac{1}{2} f_0T \)

\( f_0T \)

Q19. Motion of a particle is given by equation \( s = 3t^3 + 7t^2 + 14t + 8 \) m. The value of acceleration of the particle at \( t = 1 \) sec is Source: orcusprep.in

AIPMT 2000

easy

10 m/s^2

32 m/s^2

23 m/s^2

16 m/s^2

Q20. The position x of a particle varies with time, (t) as \( x = at^2 - bt^3 \). The acceleration will be zero at time t is equal to Source: orcusprep.in

AIPMT 1997

easy

\( \frac{a}{3b} \)

zero

\( \frac{2a}{3b} \)

\( \frac{a}{b} \)

Q21. The acceleration of a particle is increasing linearly with time t as bt. The particle starts from origin with an initial velocity \( v_0 \). The distance travelled by the particle in time t will be Source: orcusprep.in

AIPMT 1995

medium

\( v_0t + \frac{1}{2}bt^3 \)

\( v_0t + \frac{1}{2}bt^2 \)

\( v_0t + \frac{1}{6}bt^3 \)

\( v_0t + \frac{1}{3}bt^3 \)

Q22. 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 Source: orcusprep.in

AIPMT 1994

medium

3 m/s

42 m/s

-9 m/s

-15 m/s

Q23. 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 (\( g = 10 \,\text{m/s}^2 \)) Source: orcusprep.in

NEET 2020

easy

360 m

340 m

320 m

300 m

Q24. Which of the following curve does not represent
motion in one dimension ? ( For Options Check below image) Source: orcusprep.in

AIPMT 1992

easy

a

b

c

d

Q25. 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 Source: orcusprep.in

NEET 2013

medium

\( h_2 = 3h_1 \) and \( h_3 = 3h_2 \)

\( h_1 = h_2 = h_3 \)

\( h_1 = 2h_2 = 3h_3 \)

\( h_1:h_2:h_3 = 1:3:5 \)

Q26. A boy standing at the top of a tower of 20 m height drops a stone. Assuming \( g = 10 \,\text{m/s}^2 \), the velocity with which it hits the ground is Source: orcusprep.in

AIPMT 2011

easy

10.0 m/s

20.0 m/s

40.0 m/s

5.0 m/s

Q27. 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 \( t = 18 \,\text{s} \). What is the value of v? (Take \( g = 10 \,\text{m/s}^2 \)) Source: orcusprep.in

AIPMT 2010

hard

75 m/s

55 m/s

40 m/s

60 m/s

Q28. 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 Source: orcusprep.in

AIPMT 2009

easy

\( S_2 = 3S_1 \)

\( S_2 = 4S_1 \)

\( S_2 = S_1 \)

\( S_2 = 2S_1 \)

Q29. A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 m/s to 20 m/s while passing through a distance 135 m in t second. The value of t is Source: orcusprep.in

AIPMT 2008

medium

12 s

9 s

10 s

1.8 s

Q30. The distance travelled by a particle starting from rest and moving with an acceleration \( \frac{4}{3} \,\text{m/s}^2 \), in the third second is Source: orcusprep.in

AIPMT 2008

medium

\( \frac{10}{3} \) m

\( \frac{19}{3} \) m

6 m

4 m

Q31. Two bodies A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is Source: orcusprep.in

AIPMT 2006

easy

4/5

5/4

12/5

5/12

Q32. A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise? (Take \( g = 10 \,\text{m/s}^2 \)) Source: orcusprep.in

AIPMT 2005

medium

10 m

5 m

15 m

20 m

Q33. 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 \( g = 9.8 \,\text{m/s}^2 \)) Source: orcusprep.in

AIPMT 2003

hard

more than 19.6 m/s

at least 9.8 m/s

any speed less than 19.6 m/s

only with speed 19.6 m/s

Q34. If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is Source: orcusprep.in

AIPMT 2003

medium

ut

\( \frac{1}{2}gt^2 \)

\( ut - \frac{1}{2}gt^2 \)

\( (u + gt)t \)

Q35. A particle is thrown vertically upward. Its velocity at half of the height is 10 m/s, then the maximum height attained by it (\( g = 10 \,\text{m/s}^2 \)) Source: orcusprep.in

AIPMT 2001

medium

8 m

20 m

10 m

16 m.

Q36. 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? Source: orcusprep.in

AIPMT 1998

medium

4 m

6 m

8 m

2 m

Q37. If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s, it covers a distance of Source: orcusprep.in

AIPMT 1997

easy

1440 cm

2980 cm

20 m

400 m

Q38. A body dropped from a height h with initial velocity zero, strikes the ground with a velocity 3 m/s. Another body of same mass dropped from the same height h with an initial velocity of 4 m/s. The final velocity of second mass, with which it strikes the ground is Source: orcusprep.in

AIPMT 1996

medium

5 m/s

12 m/s

3 m/s

4 m/s.

Q39. The water drop falls at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at instant the first drop touches the ground. How far above the ground is the second drop at that instant? Source: orcusprep.in

AIPMT 1995

medium

3.75 m

4.00 m

1.25 m

2.50 m.

Q40. A car accelerates from rest at a constant rate \( \alpha \) for some time after which it decelerates at a constant rate \( \beta \) and comes to rest. If total time elapsed is t, then maximum velocity acquired by car will be Source: orcusprep.in

AIPMT 1994

hard

\( \frac{2\alpha\beta}{\alpha-\beta}t \)

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

\( \frac{\alpha+\beta}{\alpha\beta}t \)

\( \frac{\alpha\beta}{\alpha+\beta}t \)

Q41. The velocity of train increases uniformly from 20 km/h to 60 km/h in 4 hours. The distance travelled by the train during this period is Source: orcusprep.in

AIPMT 1994

easy

160 km

180 km

100 km

120 km

Q42. In some appropriate units, time \(t\) and position \(x\) relation of a moving particle is given by \(t = x^2 + x\). The acceleration of the particle is Source: orcusprep.in

NEET Mock 2025

hard

\( 2v^3 \)

\( -2v^3 \)

\( 2v^2 \)

\( -2v^2 \)

Q43. Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving a scooty with a speed of 60 km/h in the direction X to Y and notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses. Source: orcusprep.in

NEET Mock 2025

medium

10 min, 90 km/h

15 min, 120 km/h

9 min, 40 km/h

25 min, 100 km/h

Q44. A small block slides down on a smooth inclined plane starting from rest at time \( t=0 \). Let \( S_n \) be the distance travelled by the block in the interval \( t=n-1 \) to \( t=n \). Then the ratio \( \frac{S_n}{S_{n+1}} \) is: Source: orcusprep.in

NEET 2021

medium

\( \frac{2n-1}{2n} \)

\( \frac{2n-1}{2n+1} \)

\( \frac{2n}{2n+1} \)

\( \frac{2n+1}{2n-1} \)

Q45. The ratio of the distances travelled by a freely falling body in the 1st, 2nd, 3rd, and 4th second is: Source: orcusprep.in

NEET 2022

easy

1 : 4 : 9 : 16

1 : 3 : 5 : 7

1 : 1 : 1 : 1

1 : 2 : 3 : 4

Q46. 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 Source: orcusprep.in

NEET 2022

easy

1 : 1

1 : 2

1: \( \sqrt{3} \)

\( \sqrt{3} \) : 1.

Q47. A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \( 4 \,\text{m/s} \). The ball strikes the water surface after \( 4 \,\text{s} \). The height of bridge above water surface is (Take \( g = 10 \,\text{m/s}^2 \)) Source: orcusprep.in

NEET 2023

medium

56 m

60 m

64 m

68 m

Q48. A bullet from a gun is fired on a rectangular wooden block with velocity \( u \). When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes \( \frac{u}{3} \). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is Source: orcusprep.in

NEET 2023

medium

27 cm

24 cm

28 cm

30 cm

Q49. A vehicle travels half the distance with speed \(v\) and the remaining distance with speed \(2v\). Its average speed is Source: orcusprep.in

NEET 2023

easy

\( \frac{V}{3} \)

\( \frac{2V}{3} \)

\( \frac{4V}{3} \)

\( \frac{3V}{4} \)

Q50. A particle is moving along the x-axis with its position (x) varying with time (t) as \( x = \alpha t^4 + \beta t^2 + \gamma t + \delta \). The ratio of its initial velocity to its initial acceleration is: Source: orcusprep.in

NEET 2024

medium

2 \( \alpha \) : \( \delta \)

\( \gamma \) : 2\( \delta \)

4 \( \alpha \) : \( \beta \)

\( \gamma \) : 2\( \beta \)

Q51. An object falls freely from height \( h \) above the ground. It travels \( \frac{5}{9} \) of the total height in the last 1s. The height \( h \) is: (use \( g = 10 \,\text{m/s}^2 \)) Source: orcusprep.in

NEET 2024

medium

5 m

25 m

45 m

58 m

Q52. The velocity (v)− time (t) plot of the motion of a body is shown below:(in image)

The acceleration (a)− time (t) graph that best suits this motion is : [2024]

Source: orcusprep.in

NEET 2024

easy

a

b

c

d

Q53. The speed (s) of a car as a function of time (t) is shown figure, The distance travelled by the car in 8 seconds is: Source: orcusprep.in

easy

180

60

80

10

Q54. The position-time (x - t) graph for positive acceleration is: (for options refer below image) Source: orcusprep.in

NEET 2022

easy

a

b

c

d

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Physics - Motion in a Straight Line-PYQ

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Physics - Motion in a Straight Line-PYQ

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