Q. A bob of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1}$. As a function of $t$, the instantaneous power delivered to the body is

A) $\frac{mv_{1}t}{t_{2}}$
B) $\frac{mv_{1}t}{t_{1}}$
C) $\frac{mv_{1}t^{2}}{t_{1}}$
D) $\frac{mv_{1}^{2}t}{t_{1}^{2}}$
Explanation

(d) From $v = u + at,v_{1} = 0 + at_{1}\ \ \ \left( \because a = \frac{v_{1}}{t_{1}} \right)$
$F = ma = mv_{1}/t_{1}$
Velocity acquired in $t$ sec $= at = \frac{v_{1}}{t_{1}}t$
Power $= F \times v = \frac{mv_{1}}{t_{1}} \times \frac{v_{1}t}{t_{1}} = \frac{mv_{1}^{2}t}{t_{1}^{2}}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.