A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time, is given by

We know that,

$P_{inst}=F_{inst}\times v_{inst}$

Force is constant since the acceleration was constant.

$F_{inst}=F_{const}=ma$

$a=\frac{v}{T}$

$v_{inst}=(a\times t)$

$v_{inst}=\frac{v}{T}\times t$

$$\begin{gathered} P_{inst}=\left(m\times \frac{v}{T}\right)\times \left(\frac{v}{T}\times t\right) \\ \Rightarrow P_{inst}=\frac{m{v}^2}{T^2}t \end{gathered}$$

Hence the correct answer is $\frac{m{v}^2}{T^2}t.$