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

$A$ particle of mass $m$ describes a circle of radius $r$. The centripetal acceleration of the particle is $4/r^2$. What will be the momentum of the particle?

$A$ particle moves along an arc of a circle of radius $R$. Its velocity depends on the distance covered as $v = a\sqrt{s}$,where $a$ is a constant. Then the angle $\alpha$ between the vector of the total acceleration and the vector of velocity as a function of $s$ will be:

$A$ cyclist is riding with a speed of $27 \; km/h$. As he approaches a circular turn on the road of radius $80 \; m$,he applies brakes and reduces his speed at the constant rate of $0.50 \; m/s^2$. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

$A$ point $P$ moves in a counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length $s = t^3 + 5$,where $s$ is in meters and $t$ is in seconds. The radius of the path is $20 \ m$. The acceleration of $P$ when $t = 2 \ s$ is nearly .......... $m/s^2$.

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