Q 11-05-183JEE MainJEE Main 2019 (8 Apr, Shift 1)Easy
A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled $3\ \text{m}$ is
Answer: (C) $6.5\ \text{J}$
By the work-energy theorem, the kinetic energy gained equals the area under the force-distance graph:
$$W = \underbrace{2\times2}_{0\ \text{to}\ 2\ \text{m}} + \underbrace{\tfrac12(2+3)\times1}_{2\ \text{to}\ 3\ \text{m}} = 4 + 2.5 = 6.5\ \text{J}$$
Starting from rest, $K = 6.5\ \text{J}$.
Solution by Sreeraj P, M.Sc Physics