Question

A body of mass m kg initially at rest attains a velocity of $vm/s$ in time t under the action of a constant force F. The power supplied to the mass is:

• A. $\frac{mv}{t}$
• B. $\frac{m{v}^2}{t}$
• C. $Fv$
• D. $\frac{Fv}{2}$

Answer 1

The correct option is D $\frac{Fv}{2}$

Instantaneous velocity at some time is given by $v^{\prime }=a{t}^{\prime }=\frac{F}{m}{t}^{\prime }$

Thus average power supplied to the mass=$\frac{{\int }_0^{t}F{v}^{\prime }d{t}^{\prime }}{{\int }_0^{t}d{t}^{\prime }}$

$=\frac{F^{2}t}{2m}$

we know that $v=at=\frac{F}{m}t$

Thus the average power supplied=$\frac{Fv}{2}$