Q. 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) $\frac{1}{2}m\frac{v}{t_{1}}t^{2}$
B) $m\frac{v}{t_{1}}t^{2}$
C) $\frac{1}{2}\left( \frac{mv}{t_{1}} \right)^{2}t^{2}$
D) $\frac{1}{2}m\frac{v^{2}}{t_{1}^{2}}t^{2}$
Explanation
(d) Work done $= F \times s = ma \times \frac{1}{2}at^{2}\left\lbrack from\ s = ut + \frac{1}{2}at^{2} \right\rbrack$
$\therefore W = \frac{1}{2}ma^{2}t^{2} = \frac{1}{2}m\left( \frac{v}{t_{1}} \right)^{2}t^{2}\left\lbrack As\ a = \frac{v}{t_{1}} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.