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JEE Main 2026 (28 Jan, Shift 1) · Inertia, First & Second Laws

Inertia, First & Second Laws question from JEE Main 2026 (28 Jan, Shift 1)

Q4JEE Main 2026 · 28 JAN · SHIFT 1Difficult

Inertia, First & Second Laws

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 $(t)$ ?

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Answer: (d)

$m\frac{dv}{dt} = mg - kv$ , with $v = 0$ at $t = 0$ .
Solving: $v = \frac{mg}{k}\left(1 - e^{-kt/m}\right)$
$v$ rises from 0 with decreasing slope and levels off at terminal speed $\frac{mg}{k}$ .
So the answer is (d).

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