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Physics · Motion in one Dimension

JEE Main 2026 — 28 January, Morning Shift — Question 40

A particle of mass m falls from rest through a resistive medium having resistive force, F=−kv\mathrm{F}=-\mathrm{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 ) ?

  1. Option A:
    Option A figure
  2. Option B:
    Option B figure
    Correct
  3. Option C:
    Option C figure
  4. Option D:
    Option D figure

Answer: B

Step-by-step solution

m⋅dvdt=mg−kv\mathrm{m} \cdot \frac{\mathrm{dv}}{\mathrm{dt}}=\mathrm{mg}-\mathrm{kv}

∫0vdvmg−kv=∫0tdt m−1kln⁡(mg−kvmg)=t mv=mgk(1−e−kt/m)\begin{aligned} & \int_{0}^{\mathrm{v}} \frac{\mathrm{dv}}{\mathrm{mg}-\mathrm{kv}}=\int_{0}^{\mathrm{t}} \frac{\mathrm{dt}}{\mathrm{~m}} & \frac{-1}{\mathrm{k}} \ln \left(\frac{\mathrm{mg}-\mathrm{kv}}{\mathrm{mg}}\right)=\frac{\mathrm{t}}{\mathrm{~m}} & \mathrm{v}=\frac{\mathrm{mg}}{\mathrm{k}}\left(1-\mathrm{e}^{-\mathrm{kt} / \mathrm{m}}\right) \end{aligned}

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
28 January, Morning Shift
Subject
Physics
Chapter
Motion in one Dimension
Topic
Uniformly Accelerated Motion

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