A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 × 10⁻⁴ J by the end of the second revolution after the beginning of the motion?

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

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1.$ On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2.$ The time taken by her to walk up on the moving escalator will be

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $D.$ The height $h$ is equal to

A ball is thrown vertically downward with a velocity of $20$ m/s from the top of a tower. It hits the ground after some time with a velocity of $80$ m/s. The height of the tower is $(g = 10$ m/s$^2):$

A small block slides down on a smooth inclined plane, starting from rest at time $t=0.$ Let $S_n$ be the distance travelled by the block in the interval $t=n−1$ to $t=n.$ Then, the ratio $\frac{S_n}{S_{n+1}}$ is:

The ratio of the distance travelled by a freely falling body in the $1^{st}, 2^{nd}, 3^{rd}$ and $4^{th}$ second is:

A vehicle travels half the distance with speed $v$ and the remaining with speed $2v.$ Its average speed is:

A bullet from a gun is fired on a rectangular wooden block with velocity $u.$ When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}.$ Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m/s. The ball strikes the water surface after 4s. The height of the bridge above the water surface is (Take $g = 10$ m/s$^2$):

The velocity (v) - time (t) plot of the motion of a body is shown below. The acceleration (a) - time (t) graph that best suits this motion is: