Question

A body of mass m accelerates uniformly from rest to velocity $v_1$ 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. $\frac{m{v}_1^2{t}^2}{t_1^2}$
• D. $\frac{m{v}_1{t}^2}{t_1}$

Answer 1

The correct option is B

$\frac{m{v}_1^{2}t}{t_1^2}$

From the first equation of motion,
$v_1=0+a{t}_1\Rightarrow a=\frac{v_1}{t_1}$
Now, velocity of the body at any time t is given by $v=at=\frac{v_{1}t}{t_1}$
Instantaneous power delivered, $P=Fv=mav=m\times \frac{v_1}{t_1}\times \frac{v_{1}t}{t_1}=\frac{m{v}_1^{2}t}{t_1^2}$
Hence, the correct choice is (b).