Motion in a Straight Line · Question 18

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

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