Motion in a Straight Line

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On another day, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be

1. t1t2t2-t1
2. t1t2t2+t1
3. t1-t2
4. t1+t22

If the velocity of a particle is v = At + Bt2, where A and B are constants, then the distance travelled by it between 1 s and 2 s is

1. 32A + 73B
2. A2 + B3
3. 32A + 4B
4. 3A + 7B

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xP(t) = (at + bt2) and xQ(t) = (ft - t2). At what time do the cars have the same velocity ?

1. a-f1+b
2. a+f2(b-1)
3. a+f2(1+b)
4. f-a2(1+b)

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