Q. A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1}$. As a function of time $t$, the instantaneous power delivered to the body is
A) $\frac{mv_{1}t}{t_{1}}$
B) $\frac{mv_{1}^{2}t}{t_{1}}$
C) $\frac{mv_{1}t^{2}}{t_{1}}$
D) $\frac{mv_{1}^{2}t}{t_{1}^{2}}$
Explanation
(d) $P = \overrightarrow{F}.\overrightarrow{v} = ma \times at = ma^{2}t$ [as $u = 0$]
$= m\left( \frac{v_{1}}{t_{1}} \right)^{2}\ t = \frac{mv_{1}^{2}t}{t_{1}^{2}}$ [As $a = v_{1}/t_{1}$]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.