Question

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

• A. $\frac{m{v}_{1}t}{t_2}$
• B. $\frac{m{v}_1^{2}t}{t_1}$
• C. $\frac{m{v}_1{t}^2}{t_1}$
• D. $\frac{m{v}_1^{2}t}{t_1^2}$

Answer 1

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

From $v=u+at,v_1=0+a{t}_1$

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

$F=ma=m{v}_1/t_1$

Velocity acquired in t sec$=at=\frac{v_1}{t_1}t$

$Power=F\times v=\frac{m{v}_1}{t_1}\times \frac{v_{1}t}{t_1}=\frac{m{v}_1^{2}t}{t_1^2}$