Q 11-05-136JEE MainJEE Main 2021 (27 Jul, Shift 2)Medium
An automobile of mass $m$ accelerates starting from the origin and initially at rest, while the engine supplies constant power $P$. The position is given as a function of time by:
Answer: (D) $\left(\dfrac{8P}{9m}\right)^{\frac12}t^{\frac32}$
Work–energy: $\dfrac12mv^2 = Pt \Rightarrow v = \sqrt{\dfrac{2P}{m}}\,t^{1/2}$.
$$x = \int_0^t v\,dt = \sqrt{\frac{2P}{m}}\cdot\frac23t^{3/2} = \left(\frac{8P}{9m}\right)^{1/2}t^{3/2}$$
Solution by Sreeraj P, M.Sc Physics