Question

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

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

Answer 1

The correct option is B $\frac{m{v}_1^{2}t}{t_1^2}$

Given a mass $m$ acquiring velocity $v_1$ from rest in time $t_1$

The acceleration of the particle will be

$a$ = $\frac{v_1-u}{t_1}$

$a$ = $\frac{v_1}{t_1}$

The velocity of the particle at any time $t$ will be

$v=u+at$

$v=at$

The instantaneous power is given by

$P$ = $Fv$ (force times the instantaneous velocity)

$P$ = $mav$

$P$ = $m{a}^{2}t$

$P$ = $\frac{m{v_1}^2}{{t_1}^2}t$