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. $\frac{m{v}_1^{2}t}{t_1}$
• B. $\frac{m{v}_{1}t}{t_1}$
• C. $\frac{m{v}_1{t}^2}{t_1}$
• D. $\frac{m{v}_1^{2}t}{t_1^2}$

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
$=Fv=m\frac{v_1}{t_1}\times \frac{v_1}{t_1}t$
$=\frac{m{v}_1^{2}t}{t_1^2}$