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Physics · Motion in one Dimension

JEE Main 2024 — 29 January, Shift 1 — Question 34

A body starts moving from rest with constant acceleration covers displacement S1S_{1} in first ( p−1p-1 ) seconds and S2\mathrm{S}_{2} in first p seconds. The displacement S1+S2\mathrm{S}_{1}+\mathrm{S}_{2} will be made in time :

  1. Option A:

    (2p+1)s(2 p+1) s

  2. Option B:

    (2p2−2p+1)s\sqrt{\left(2 \mathrm{p}^{2}-2 \mathrm{p}+1\right)} \mathrm{s}

    Correct
  3. Option C:

    (2p−1)s(2 p-1) s

  4. Option D:

    (2p2−2p+1)s\left(2 p^{2}-2 p+1\right) s

Answer: B

Step-by-step solution

S1\mathrm{S}_{1} in first (p−1)sec(\mathrm{p}-1) \mathrm{sec}

S2\mathrm{S}_{2} in first p sec

S1=12a(p−1)2S_{1}=\frac{1}{2} a(p-1)^{2}

S2=12a(p)2\mathrm{S}_{2}=\frac{1}{2} \mathrm{a}(\mathrm{p})^{2} S1+S2=12at2\mathrm{S}_{1}+\mathrm{S}_{2}=\frac{1}{2} \mathrm{at}^{2} (p−1)2+p2=t2(\mathrm{p}-1)^{2}+\mathrm{p}^{2}=\mathrm{t}^{2}

t=2p2+1−2p\mathrm{t}=\sqrt{2 \mathrm{p}^{2}+1-2 \mathrm{p}}

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
29 January, Shift 1
Subject
Physics
Chapter
Motion in one Dimension
Topic
Uniformly Accelerated Motion