Q 11-05-159JEE MainJEE Main 2020 (5 Sep, Shift 2)Medium
A body of mass $2$ kg is driven by an engine delivering a constant power of $1\ \text{J s}^{-1}$. The body starts from rest and moves in a straight line. After $9$ s, the body has moved a distance (in m) ______.
Numerical value type. Enter your answer.
Answer: 18
Work done by the engine equals the kinetic energy gained:
$$Pt = \tfrac12 mv^2 \Rightarrow v = \sqrt{\frac{2Pt}{m}} = \sqrt{t}\ \text{m/s}$$
$$x = \int_0^9 \sqrt t\,dt = \frac23 t^{3/2}\Big|_0^9 = \frac23\times27 = 18\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics