Q 11-04-062JEE MainJEE Main 2026 (28 Jan, Shift 1)Easy
A particle of mass $m$ falls from rest through a resistive medium having resistive force, $F = -kv$, where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity $(v)$ versus time $(t)$ ?
Answer: (D) see figure
$$m\frac{dv}{dt} = mg - kv$$
Starting from $v = 0$:
$$v = \frac{mg}{k}\left(1 - e^{-kt/m}\right)$$
The velocity starts at zero, rises steeply at first (slope $g$) and then flattens out, approaching the terminal velocity $mg/k$. This is graph (D).
Solution by Sreeraj P, M.Sc Physics