Q 11-05-021JEE MainEAMCET 2012 (Engineering)Medium
The velocity $v$ reached by a car of mass $m$ on moving a certain distance from the starting point, when driven by a motor with constant power $P$, is such that
Answer: (C) $v^3 \propto \dfrac{3P}{m}$
With constant power, $P = Fv = mv\dfrac{dv}{dt}$, and $\dfrac{dv}{dt} = v\dfrac{dv}{dx}$, so:
$$P = mv^2\frac{dv}{dx} \;\Rightarrow\; \int_0^v v^2\,dv = \frac{P}{m}\int_0^x dx \;\Rightarrow\; v^3 = \frac{3P}{m}x$$
For a given distance, $v^3 \propto \dfrac{3P}{m}$.
Solution by Sreeraj P, M.Sc Physics