# Work done in time t on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by

$\begin{array}{1 1}\large\frac{1}{2}\normalsize m\large\frac{v}{t_1}\normalsize t^2\\ m\large\frac{v}{t_1}\normalsize t^2\\\large\frac{1}{2}\big(\frac{mv}{t_1}\big)^2\normalsize t^2\\\large\frac{1}{2}\normalsize m\large\frac{v^2}{t_1^2}\normalsize t^2\end{array}$

Answer : $\large\frac{1}{2}\normalsize m\large\frac{v^2}{t_1^2}\normalsize t^2$
Work done =$F.s=ma\big(\large\frac{1}{2}$$at^2\big) \qquad\qquad\qquad =\large\frac{1}{2}$$ma^2t^2$
As acceleration $(a)=\large\frac{v}{t_1}$
$\qquad\qquad\qquad= \large\frac{1}{2}\normalsize m\large\frac{v^2}{t_1^2}\normalsize t^2$