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).

$A$ car is moving with speed $30 \,m/s$ on a circular path of radius $500 \,m$. Its speed is increasing at a rate of $2 \,m/s^2$. What is the total acceleration of the car (in $\,m/s^2$)?

$A$ particle moves in a circular path of radius $r$ with speed $v.$ It then increases its speed to $2v$ while travelling along the same circular path. The centripetal acceleration of the particle has changed by a factor of

The tangential acceleration of a particle moving in a circle of radius $1 \ m$ varies with time $t$ as shown in the graph (initial velocity of the particle is zero). The time after which the total acceleration of the particle makes an angle of $30^{\circ}$ with the radial acceleration is:

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

$A$ 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?