Question

An object of mass $m$, initially at rest under the action of a constant force $F$ attains a velocity $v$ in time $t$. Then, the average power supplied to mass is

• A. $\frac{m{v}^2}{2t}$
• B. $\frac{Fv}{2}$
• C. Both $a$ and $b$ are correct
• D. Both $a$ and $b$ are wrong

Answer 1

The correct option is C Both $a$ and $b$ are correct

Impulse $p=Ft$
$W=KE=\frac{p^2}{2m}=\frac{F^2{t}^2}{2m}$
$=\frac{\left(\frac{F}{m}\right)t.Ft}{2}$
$=\frac{\left(at\right)Ft}{2}=\frac{Fvt}{2}$
$\therefore$ Average power $=\frac{W}{t}=\frac{F.v}{2}$
Average power = $\frac{KE}{t}=\frac{m{v}^2}{2t}$