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) $v^3 \propto \dfrac{3P}{m}$
Concept. Constant power: $P = mv^2\dfrac{dv}{dx}$.
Step 1. Integrate. $\dfrac{v^3}{3} = \dfrac Pmx \Rightarrow v^3 = \dfrac{3P}{m}x$.
Answer. $v^3 \propto \dfrac{3P}{m}$ (Option C).
Solution by Sreeraj P, M.Sc Physics