$A$ 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 $\,m/s^2$)?

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 $m/s$?

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:

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:

$A$ particle is moving in a circle of radius $50 \ cm$ in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at $t=0$ is $4 \ m/s$,the time taken to complete the first revolution will be $\frac{1}{\alpha}[1-e^{-2 \pi}] \ s$,where $\alpha=$ . . . . . . .

The angular speed of a particle moving in a circular path is doubled. Then, the centripetal acceleration of the particle is