JEE Main 2026 — Jan 28, Shift 1 — Physics solution

JEE Main2026Jan 28, Shift 1Physics

A particle of mass m falls from rest through a resistive medium having resistive force, $F = - k v$ , where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity (v) versus time(t) ?

A
Graph (1)
B
Graph (2)
C
Graph (3)
D
Graph (4)

Solution

Equation of motion: $m \frac{d v}{d t} = m g - k v$ .

Separating variables and integrating with $v (0) = 0$ :

$\int_{0}^{v} \frac{d v ^{'}}{m g - k v ^{'}} = \int_{0}^{t} \frac{d t ^{'}}{m}$

$- \frac{1}{k} ln (\frac{m g - k v}{m g}) = \frac{t}{m}$

$v (t) = \frac{m g}{k} (1 - e^{- k t / m})$ .

This is a saturating exponential rise from $0$ to terminal velocity $v_{t} = m g / k$ . Option (2).

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