Problem 1.126

A particle of mass \(m\) moves along a circle of radius \(R\) with a normal acceleration varying with time as \(w_{n}=a t^{2},\) where \(a\) is a constant. Find the time dependence of the power developed by all the forces acting on the particle, and the mean value of this power averaged over the first \(t\) seconds after the beginning of motion.