A particle of mass M is moving in a circle of fixed radius ‘R’ in such a way that its centripetal acceleration at time ‘t’ is given by $n^{2}R{t}^2$ . Where n is a constant,  the power delivered to the particle by the force acting on it is 

$\therefore$   Centripetal Acceleration =   $n^{2}R{t}^2=\frac{{V_t}^2}{R}$
   $$\begin{gathered} \therefore {V_t}^2=n^2{R}^2{t}^2\Rightarrow V_t=nRt---\left(1\right) \\ differentiate with respect to time t \\ \frac{d{V}_t}{dt}=nR---\left(2\right) \end{gathered}$$
   $$\begin{gathered} Tangential Force on the particle is F_t=M\frac{d{V}_t}{dt} \\ substitute equation \left(2\right) \\ {F}_t=M n R---\left(3\right) \\ here V_t is speed of the particle \end{gathered}$$ 
   $$\begin{gathered} power delivered =F_t\cdot V_t \\ substitute equations \left(3\right) and \left(1\right) in above equation \\ \text{\hspace{0.17em} power delivered =}=MnR\cdot nRt=M{n}^2{R}^2\cdot t \end{gathered}$$