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. $\frac{MV^2}{T}$
• B. $\frac{1}{2}\frac{MV^2}{T^2}$
• C. $\frac{MV^2}{T^2}$
• D. $\frac{1}{2}\frac{MV^2}{T}$

Answer 1

Answer: (D)

Power delivered in time $T$ is
$ P=F \cdot V=M a V $
or $ P=M V \frac{d V}{d T}$
$ \Rightarrow P d T=M V d V$
$\Rightarrow P T=\frac{M V^{2}}{2} $
or $ P=\frac{1 M V^{2}}{2} T$