Question

A body of mass $ m $ accelerates uniformly from rest to $ v_1 $ in the time $ t_1 $ . The instantaneous power delivered to the body as a function of time

• A. $ \frac{mv^{2}_{1}t}{t_{1}} $
• B. $ \frac{mv_{1}t}{t_{1}} $
• C. $ \frac{mv_{1}t^{2}}{t_{1}} $
• D. $ \frac{mv^{2}_{1}t}{t_{1}^{2}} $

Answer 1

Answer: (D)

Acceleration of the body,
$a = \frac{v_1 - 0}{t_1 -0} = \frac{v_1}{t_1}$
[$\because$ Body was initially at rest]
Force on the body, $F = ma = m \frac{v_1}{t_1}$
Instantaneous velocity of the body,
$v = at = \frac{v_1}{t_1} t$
Instantaneous power
$ = Fv = m \frac{v_1}{t_1} \times \frac{v_1}{t_1} t $
$ = \frac{mv_1^2 t}{t_1^2}$