NEET AIPMT Physics Chapter Wise Solutions – Motion in a Straight Line

NEET AIPMT Physics Chapter Wise Solutions – Motion in a Straight Line

NEET AIPMT Physics Chapter Wise SolutionsChemistryBiology

1. A particle of unit mass undergoes one¬dimensional motion such that its velocity varies according to v(x) = βx^-2n, where β 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) -2β² x ²ⁿ⁺¹
(b) -2nβ²e ^-4n+1
(c) -2nβ² x ^2n-1
(d) -2nβ²x^-4n-1  (AIPMT 2015, Cancelled)

2. A stone falls freely under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁, h₂ and h₃ is
(a) h2 = 3h₁ and h3 = 3h2
(b) h₁= h2= h3
(C) h₁ = 2h2 = 3h3
(d) h₁=  = (NEET 2013)

3. 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 = + 3 The displacement of the particle when its velocity is zero, will be
(a) 4m
(b) 0m(zero)
(c) 6 m
(d) 2 m (Karnataka NEET 2013)

4. The motion of a particle along a straight line is described by equation x = 8 + 12t – t³ where x is in metre and / in second. The retardation of the particle when its velocity becomes zero is
(a) 24 ms^-2
(b) zero
(c) 6ms^-2
(d) 12ms^-2  (Prelims 2012)

5. A boy standing at the top of a tower of 20 m height drops a stone. Assuming g= 10 m s^-2 , the velocity with which it hits the ground is
(a) 10.0 m/s
(b) 20.0 m/s
(c) 40.0 m/s
(d) 5.0 m/s(Prelims 2011)

6. A particle covers half of its total distance with speed v₁ and the rest half distance with speed v2. Its average speed during the complete journey is

7. A particle moves a distance x in time / according to equation x = (/ + 5)^-1. The acceleration of particle is proportional to
(a) (velocity)^3/2
(b) (distance)2
(c) (distance) 2
(d) (velocity)^2/3 (Prelims 2010)

8. 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 s. What is the value of v? (Takeg= 10 m/s²)
(a) 75 m/s
(b) 55 m/s
(c) 40 m/s
(d) 60 m/s ( Prelims 2010)

9. A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is 5, and that covered in the first 20 seconds is S2 , then
(a) S2 = 3s₁
(b)S₂ = 4s₁
(c) S₂=s₁
(d) S₂ = 2s₁ (Prelims 2009)

10. A bus is moving with a speed of 10 ms^-1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?
(a) 40 ms^-1
(b) 25 ms^-1
(c) W) ms^-1
(d) 20 ms^-1 (Prelims 2009)

11. 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 (Prelims 2008)

12. The distance travelled by a particle starting from 4-2 rest and moving with an acceleration -j ms , in the third second is
(a) Ym
(b) Tm
(c) 6m
(d) 4m (Prelims 2008 )

13. A particle moving along x-axis has acceleration f, at time t, given by f= fo() , where f0 and T are constants. The panicle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when t= 0, the particle’s velocity (v_x).

14. A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip IS

15. The position x of a particle with respect to time t along x-axis is given by x = 9¹² – t³ 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?
(a) 54 m
(b) 81m
(c) 24m
(d) 32m. (2007)

16. 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
(a) 4/5
(b) 5/4
(c) 12/5
(d) 5/12. (2006)

17. 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
(a) 10 m/s, 0
(b) 0, 0
(c) 0, 10 m/s
(d) 10 m/s, 10 m/s. (2006)

18. 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 + 12t²— t³. How long would the particle travel before coming to rest?
(a) 16 m
(b) 24 m
(c) 40 m
(d) 56 m. (2006)

19. 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 m/s²
(a) 10 m
(b) 5 m
(c) 15 m
(d) 20 m. (2005)

20. The displacement x of a particle varies with time t as x =ae^-αt+ be^βt where a,b, a and P are positive constants. The velocity of the particle will
(a) be independent of β
(b) drop to zero when α = β
(c) go on decreasing with time
(d) go on increasing with time. (2005)

21. 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 m/s²)
(a) more than 19.6 m/s
(b) at least 9.8 m/s
(c) any speed less than 19.6 m/s
(d) only with speed 19.6 m/s. (2003)

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

23. 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 m/s²)
(a) 8 m
(b) 20 m
(c) 10 m
(d) 16 m. (2001)

24. Motion of a particle is given by equation i = (3t³ + 7t²– + 14t + 8) m. The value of acceleration of the particle at / = 1 sec is
(a) 10 m/s²
(b) 32 m/s²
(c) 23 m/s²
(d) 16 m/s². (2000)

25. A car moving with a speed of 40 km/h can be stopped by applying brakes after at least 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance?
(a) 4 m
(b) 6 m
(c) 8m
(d) 2 m. (1998)

26. A rubber ball is dropped from a height of 5 m on a plane. On bouncing it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of

27. The position x of a particle varies with time, (t) as x = at² – bt³. The acceleration will be zero at time t is equal to

28. If a car at rest accelerates uniformly to a speed of 144 km/h in 20 sec, it covers a distance of
(a) 1440 cm
(b) 2980 cm
(c) 20m
(d) 400m. (1997)

29. 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
(a) 5 m/s
(b) 12 m/s
(c) 3 m/s
(d) 4 m/s. (1996)

30. The acceleration of a particle is increasing linearly with time t as bt. The particle starts from origin with an initial velocity V₀. The distance travelled by the particle in time t will be

31. The water drop fells 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?
(a) 3.75 m
(b) 4.00 m
(c) 1.25 m
(d) 2.50m. (1995)

32. A car accelerates from rest at a constant rate a for some time after which it decelerates at a constant rate p and comes to rest. If total time elapsed is t, then maximum velocity acquired by car will be

33. A particle moves along a straight line such that its displacement at any time t is given by s = (t³ – 6t² + 3t+ 4) metres. The velocity when the acceleration is zero is
(a) 3 m/s
(b) 42 m/s
(c) – 9 m/s
(d) – 15 m/s. (1994)

34. 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
(a) 160km
(b) 180km
(c) 100km
(d) 120km. (1994)

35. 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. (1994)

36. A body starts from rest, what is the ratio of the distance travelled by the during the 4^th and 3^rd second ?
(a)
(b)
(c)
(d)  (1993)

37. Which of the following curve does not represent motion in one dimension ?

38. A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is (g = 10 m/s²)
(a) 60 m
(b) 45 m
(c) 80 m
(d) 50 m. (1992)

39. 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
(a) 56 km/h
(b) 60 km/h
(c) 50 km/h
(d) 48 km/h. (1991)

40. 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
(a) 9 km/h
(b) 16 km/h
(c) 18 km/h
(d) 48 km/h. (1991)

41. 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
(a) 40 km/h
(b) 48 km/h
(c) 50 km/h
(d) 60 km/h. (1990)

42. What will be the ratio of the distance moved by a freely falling body from rest in 4^th and 5^th seconds of journey ?
(a) 4:5
(b) 7 : 9
(c) 16:25
(d) 1:1. (1989)

43. A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 km/ h and 40 km/h respectively. The velocity of the car midway between P and Q is
(a) 33.3 km/h
(b) 20 km/h
(c) 25 km/h
(d) 35 km/h. (1988)

Explanations