Question

A particle of mass m is rotating in a circle of radius r with power p=mk2r2t2p=mk2r2t2. Find the centripetal acceleration.

Answer 1

p= force*velocity =
$force \times v = m {k}^{2} {r}^{2} {t}^{2}$
Now, power is only provided by tangential force and not by centripetal force as tangential force is in directioj of velocity and centripetal force is perpendicular to the direction of velocity
So, mvdv/dt = m {k}^{2} {r}^{2} {t}^{2}
By integrating on both sides
v^2 = 2/3 * {k}^{2} {r}^{2} {t}^{3}
So, centripetal acceleration = mv^2/r