Velocity proportionality under constant power – Rankers Physics

Power: Practice Problem & Solution

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: (2012 Mains)
$t^2 P_0$
$t^{1/2}$
$t^{-1/2}$
$\frac{1}{\sqrt{m}}$

Solution Explained:

To solve this problem, we apply the core principles of Power. Understanding the underlying formula is key to arriving at the correct answer below:

From constant power $P_0 = mv\frac{dv}{dt}$, integrate both sides to get $v^2 = \frac{2P_0 t}{m}$. Thus, velocity $v \propto t^{1/2}$.

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