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

$\text{Average Power}$
$=\frac{\text{Work done}}{\text{time}}$
$=\frac{\text{change in kinetic energy}}{\text{time}}$
$=\frac{(K{E}_f-K{E}_i)}{t}$
$=\frac{\frac{1}{2}m{v}^2-0}{t}$
$=\frac{m{v}^2}{2t}$
$=\frac{m(at{)}^2}{2t}$ (Since $v=at$)
$=\frac{\left(ma\right)\left(at\right)}{2}$
$=\frac{Fv}{2}$ (Since $F=ma$)