Q. A body of mass $m$accelerates uniformly from rest to $v_{1}\ $is time$\ t_{1}$. The instantaneous power delivered to the body as a function of time t is
A) $\frac{mv_{1}t}{t_{1}}$
B) $\frac{mv_{1}^{2}t}{t_{1}^{2}}$
C) $\frac{mv_{1}t^{2}}{t_{1}}$
D) $\frac{mv_{1}^{2}t}{t_{1}}$
Explanation
(b) Let the constant acceleration of body of mass m is a,
From equation of motion
$v_{1} = 0 + at_{1}$
Or $a = \frac{v_{1}}{t_{1}}$ …(i)
At an instant t, the velocity v of the body
$v = 0 + at$
$v = \frac{v_{1}}{t_{1}}t$ …(ii)
Therefore, instantaneous power
$p = Fv = mav$
$= m\left( \frac{v_{1}}{t_{1}} \right) \times \left( \frac{v_{1}}{t_{1}}.t \right)\ \ \ \ $ [From Eqs.(i)and (ii)]
=$\frac{mv_{1}^{2}t}{t_{1}^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.