$A$ 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?

The acceleration of a body in a non-uniform circular motion is $5\, ms^{-2}$. Which one of the following is correct?

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration is varying with time as $a_c = k^2rt^2$. The power delivered to the particle by the forces acting on it is $(k = \text{constant})$

The magnitude of the centripetal force acting on a body of mass $m$ executing uniform circular motion in a circle of radius $r$ with speed $v$ is:

In a circular motion of a particle,the tangential acceleration of the particle is given by $a_t = 12 \ m/s^2$. The radius of the circle is $3 \ m$. The particle was initially at rest. The time after which the total acceleration of the particle makes an angle $45^{\circ}$ with the radial acceleration is

In non-uniform circular motion,the ratio of tangential to radial acceleration is ($r$ is the radius of the circle,$v$ is the speed of the particle,$\alpha$ is the angular acceleration).