Motion in a Straight Line · Question 20

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = x-2n, where 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

1. -2 2x-2n+1
2. -2n 2e-4n+1
3. -2n 2x-2n-1
4. -2n 2x-4n-1

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

1. h2 = 3h1 and h3 = 3h2
2. h1 = h2 = h3
3. h1 = 2h2 = 3h3
4. h1 = h23 = h35

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 = x + 3. The displacement of the particle when its velocity is zero, will be

1. 4 m
2. 0 m (zero)
3. 6 m
4. 2 m

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

1. 68%
2. 41%
3. 200%
4. 100%

The motion of a particle along a straight line is described by equation x = 8 + 12t - t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

1. 24 m s-2
2. zero
3. 6 m s-2
4. 12 m s-2

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

1. v1+v22
2. v1v2v1+v2
3. 2v1v2v1+v2
4. v12v22v12+v22

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

1. 10.0 m/s
2. 20.0 m/s
3. 40.0 m/s
4. 5.0 m/s

A particle moves a distance x in time t according to equation x = (t + 5)-1. The acceleration of particle is proportional to

1. (velocity)3/2
2. (distance)2
3. (distance)-2
4. (velocity)2/3

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? (Take g = 10 m/s2)

1. 75 m/s
2. 55 m/s
3. 40 m/s
4. 60 m/s

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then

1. S2 = 3S1
2. S2 = 4S1
3. S2 = S1
4. S2 = 2S1