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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
$t/\sqrt m$
B
$t^2P_0$
C
$t^{1/2}$
D
$t^{-1/2}$
Detailed Solution
$P_0 = Fv = m\frac{dv}{dt}v$
$v\,dv = \frac{P_0}{m}dt$
Integrating from rest: $\frac{v^2}{2} = \frac{P_0}{m}t$
$v = \sqrt{\frac{2P_0t}{m}} \Rightarrow v \propto t^{1/2}$
$v\,dv = \frac{P_0}{m}dt$
Integrating from rest: $\frac{v^2}{2} = \frac{P_0}{m}t$
$v = \sqrt{\frac{2P_0t}{m}} \Rightarrow v \propto t^{1/2}$