Question

A body of mass m, accelerates uniformly from rest to $V_1$ in time $t_1$ . The instantaneous power after 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. $\frac{m{V}_1^2{t}_1}{t}$

Answer 1

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

Using first equation of motion, velocity after time $t_1$ is given by:
$V_1=a{t}_1$

Similarly, velocity after time $t$ is:

$v=at=\frac{V_{1}t}{t_1}$

Power is given by: $P=Fv=mav$
$P=m\left(\frac{V_1}{t_1}\right)\times \left(\frac{V_{1}t}{t_1}\right)=\frac{m{V}_1^{2}t}{t_1^2}$