If the frequency of an object in uniform circular motion is doubled,its acceleration becomes

An object moves along a circle with normal acceleration proportional to $t^\alpha$, where $t$ is the time and $\alpha$ is a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to

$A$ 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 $a_c = k^2 r t^2$. The power delivered to the particle by the forces acting on it 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 ........ $rad/s$.

If the length of the second's hand in a stop clock is $3 \, cm$,the angular velocity and linear velocity of the tip are:

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 $^{\circ}$)