$A$ particle performing $U.C.M.$ of radius $\pi/2 \text{ m}$ makes $x$ revolutions in time $t$. Its tangential velocity is

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c = k^2rt^2$,where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

$A$ wheel has a speed of $1200$ revolutions per minute and is made to slow down at a rate of $4 \ rad/s^{2}$. The number of revolutions it makes before coming to rest is

$A$ racing car is travelling along a track at a constant speed of $40\ m/s$. $A$ $T.V.$ cameraman is recording the event from a distance of $30\ m$ directly away from the track as shown in the figure. In order to keep the car under view in the position shown,the angular speed with which the camera should be rotated is ........ $rad/s$.

The wheel of a car is rotating at the rate of $1200$ revolutions per minute. On pressing the accelerator for $10 \ s$,it starts rotating at $4500$ revolutions per minute. The angular acceleration of the wheel is:

$A$ particle starting from rest moves in a circle of radius $r$. It attains a velocity of $V_{0} \; m/s$ in the $n^{\text{th}}$ round. Its angular acceleration will be