Question

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

• A. $t^2 P_0$
• B. $t^{1/2}$
• C. $t^{-1/2}$
• D. $\frac{1}{\sqrt m}$

Answer 1

Answer: (B)

$t^{1/2}$

Answer 2

$P_0 =FV$
$\because \, \, \, \, F=ma=m\frac{dv}{dt}$
$\therefore \, \, \, \, \, \, P_0 =mv\frac{dv}{dt}$
or $\, \, \, \, \, \, P_0 dt =mvdv$
Integrating both sides, we get
$\int \limits_0^t \, p_0dt =m \int \limits_0^\upsilon \upsilon d\upsilon$
$p_0 t =\frac{m\upsilon ^2}{2}$
$v=\bigg(\frac{2P_0 t}{m}\bigg)^{1/2}$ or $\upsilon \propto \, \sqrt t$