A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a is varying with time t as a = k^(2)rt^(2) where k is a constant. What is the power delivered to the particle by the forces acting on it.

A particle of mass m is moving in a circular path of constant radius r

1.	A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a is varying with time t as a = k^(2)rt^(2) where k is a constant. What is the power delivered to the particle by the forces acting on it.
Answer» <P> Solution :`Asa_(c)=(v^(2)//R)so(v^(2)//r)=k^(2)rt^(2)` KINETIC energy `K = (1)/(2) mv^(2) = (1)/(2) mk^(2)r^(2)t^(2)` Now by work - Enetgy Theorem `W=DeltaK=(1)/(2)mk^(2)r^(2)t^(2)-0rArrP=(dw)/(dt)` `RARR P = (d)/(dt) = (1)/(2) mk^(2)r^(2)t^(2) =mk^(2)r^(2)t`