A particle of mass m is moving in a circular path of constant radius r such that its centripetal…

$a_c=k^{2}r{t}^2$

Or $\frac{v^2}{r}=k^{2}r{t}^2$  Or    $v=krt$
Therefore, tangential acceleration, $a_t=\frac{\mathrm{d}v}{\mathrm{d}t}=kr$

Therefore, tangential force, $F_t=m{a}_t=mkr$

Only tangential force does work.

$\text{Power}=F_{t}v=\left(mkr\right)\left(krt\right)$ $\text{⇒Power}=m{k}^2{r}^{2}t$