Problem $2$: A radar gun at $O$ rotates and follows the motion of the car traveling along the circular road

having a radius of $r=200m.$ At the instant when $=90,$ the acceleration has a magnitude of $a=10$

$\frac{m}{s^2}$ and an angular velocity of ${}^{}=0\mathrm{.}05ra\frac{d}{s}.$

At this instant,

$($a$)$ determine the speed of the car and

$($b$)$ determine the angular acceleration of the radar gun.