Question

A particle of mass $m$ is lying on smooth horizontal table. A constant force $F$ tangential to the surface is applied on it. Find average power over a time interval from $t=0$ to $t=t$.

• A. $\frac{F^{2}t}{3m}$
• B. $\frac{F^{2}t}{2m}$
• C. $\frac{2F^{2}t}{3m}$
• D. $\frac{3F^{2}t}{2m}$

Answer 1

The correct option is B $\frac{F^{2}t}{2m}$

Average power of a time interval $t=0$ to $t=t$

is $\frac{{\int }_0^{t}Fvdt}{{}_0^t\int dt}$

$=\frac{F{\int }_0^{t}vdt}{t}$

$=\frac{F{\int }_0^t\frac{F}{m}tdt}{t}$

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