A particle of mass m moving in a circular path of constant radius r such that its centripetal acceleration `a_(c)` is varying with time t as `a_(c)= k^(2)rt^(2)`, where k is a constant.

Explanation

As `a_(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 - Energy Theorem
`W=Delta K = (1)/(2)mk^(2)r^(2)t^(2)-0rArr P =(dW)/(dt)`
`rArr P=(d)/(dt)=(1)/(2)mk^(2)r^(2)t^(2)=mk^(2)r^(2)t`