Question

A body of mass m is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time, is given by :

• A. $\frac{mv^{2}}{T^{2}}t$
• B. $\frac{mv^{2}}{T^{2}}t^2$
• C. $\frac{1}{2} \,\frac{mv^{2}}{T^{2}}t$
• D. $\frac{1}{2} \,\frac{mv^{2}}{T^{2}}t^2$

Answer 1

Answer: (A)

$\frac{mv^{2}}{T^{2}}t$

Answer 2

$F=ma=\frac{mv}{T}\,\left(\therefore a=\frac{v-0}{T}\right)$ Instantaneous power$= Fv$ $=mav$ $=\frac{mv}{T}\cdot at=\frac{mv}{T}\cdot\frac{v}{T}\cdot t$ $=\frac{mv^{2}}{T^{2}}t$