Question

A particle of mass $M$, starting from rest, undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, the power delivered to the particle is

• A. $\frac{M{V}^2}{T}$
• B. $\frac{1}{2}\frac{M{V}^2}{T^2}$
• C. $\frac{M{V}^2}{T^2}$
• D. $\frac{1}{2}\frac{M{V}^2}{T}$

Answer 1

The correct option is D $\frac{1}{2}\frac{M{V}^2}{T}$

Power delivered in time T is
$P=\overrightarrow{F}\cdot \overrightarrow{V}=MaV$
or $P=MV\frac{dV}{dT}$ $\Rightarrow$ $PdT=MVdV$
$\Rightarrow PT=\frac{M{V}^2}{2}$ or $P=\frac{1}{2}\frac{M{V}^2}{T}$