• # question_answer A body of mass m accelerates uniformly from rest to a speed $\left( \lambda \right)$in time $\infty$. The work done on the body till any time t is A) $\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}^{2}}}{t_{0}^{2}} \right)$ B) $\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}_{0}}}{t} \right)$ C) $mv_{0}^{2}\left( \frac{t}{{{t}_{0}}} \right)$ D) $mv_{0}^{2}{{\left( \frac{t}{{{t}_{0}}} \right)}^{3}}$

 [a] ${{v}_{0}}=a{{t}_{0}}$        $\therefore$    $a=\frac{{{v}_{0}}}{{{t}_{{}}}}$ Velocity at any time t would be $V=at=\left( \frac{{{v}_{0}}}{{{t}_{0}}} \right)t$
 $\therefore$  Kinetic energy, $\text{K=}\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{\left( \frac{{{v}_{0}}}{{{t}_{0}}} \right)}^{2}}{{t}^{2}}$ From work energy theorem $W=K.E.$ or   $W=\frac{1}{2}mv_{0}^{2}\left( \frac{{{t}^{2}}}{t_{0}^{2}} \right)$