## 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 ^{-2}n, 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) -2β

^{2}x

^{2n+1 }(b) -2nβ

^{2}e

^{ -4n+1}

(c) -2nβ

^{2}x

^{2n-1 }(d) -2nβ

^{2}x

^{-4n-1 }

**(AIPMT 2015, Cancelled)**

**2. 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) h2 = 3h

_{1}and h3 = 3h2

(b) h

_{1}= h2= h3

(C) h

_{1}= 2h2 = 3h3

(d) h

_{1}= =

**(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 – t ^{3} 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 v _{1} 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/s ^{2})**

(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 = 3s_{1
}(b)S_{2} = 4s_{1}

(c) S_{2}=s_{1
}(d) S_{2} = 2s_{1 }**(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 = 9 ^{12} – 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?**

(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 + 12t ^{2}— t^{3}. 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/s ^{2}**

(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/s ^{2})**

(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/s ^{2})**

(a) 8 m

(b) 20 m

(c) 10 m

(d) 16 m.

**(2001)**

**24. Motion of a particle is given by equation i = (3t ^{3} + 7t^{2}– + 14t + 8) m. The value of acceleration of the particle at / = 1 sec is**

(a) 10 m/s

^{2}

(b) 32 m/s

^{2}

(c) 23 m/s

^{2}

(d) 16 m/s

^{2}.

**(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 = at ^{2} – bt^{3}. 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 V _{0}. 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 = (t ^{3} – 6t^{2} + 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/s ^{2})**

(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