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

• A
  $\frac{1}{2}m\left(\frac{v}{t_1}\right)^2 t^2$
• B
  $m\left(\frac{v}{t_1}\right)^2 t^2$
• C
  $\frac{1}{2}\left(\frac{mv}{t_1}\right)^2 t^2$
• D
  $\frac{1}{2}m\frac{v^2}{t_1^2}t^2$