$A$ particle of mass $m$ moves in a circle of radius $r$. Its centripetal acceleration changes with time according to the formula $a_c = k^2 r t^2$. What is the power delivered to the particle by the force acting on it?

$A$ car is travelling at $30 \,ms^{-1}$ speed on a circular road of radius $300 \,m$. If its speed is increasing at the rate of $4 \,ms^{-2}$, then its acceleration is (in $\,ms^{-2}$)

$A$ uniform circular disc of radius $50\, cm$ at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of $2.0\, rad \,s^{-2}$. Its net acceleration in $m\,s^{-2}$ at the end of $2.0\,s$ is approximately (in $.0$)

The angular velocity of a particle of a rigid body is not constant. Which of the following statements is true?

The acceleration of a particle performing non-uniform circular motion is shown in the diagram at point $P$. If the radius of the circular path is $2 \ m$,then what is the velocity at point $P$ in $m/s$?

$A$ car is moving with a speed of $30 \,ms^{-1}$ on a circular path of radius $500 \,m$. If its speed is increasing at the rate of $2 \,ms^{-2}$, then find its acceleration. (in $\,ms^{-2}$)