The velocity $\vec{v}$ of a particle of mass $m$ acted upon by a constant force is given by $\vec{v}(t) = A[\cos(kt) \hat{i} - \sin(kt) \hat{j}]$. Then the angle between the force and the velocity of the particle is (Here $A$ and $k$ are constants). (in $^{\circ}$)

$A$ 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 ........ $rad/s$.

$A$ merry-go-round makes $120$ revolutions per minute. $A$ child sitting on it starts crying,so the merry-go-round is slowed down with a retardation of $2 \ rad \ s^{-2}$. How long will it take for the merry-go-round to come to a stop? How many revolutions will it make before coming to a stop?

$A$ wheel rotates with a uniform angular acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions completed in the first $10 \ s$ will be approximately:

The angle turned by a body undergoing circular motion depends on time as $\theta = \theta_0 + \theta_1 t + \theta_2 t^2$. Then the angular acceleration of the body is

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