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Physics · Motion in one Dimension

JEE Main 2024 — 9 April, Shift 1 — Question 32

A particle moving in a straight line covers half the distance with speed 6 m/s6 \mathrm{~m} / \mathrm{s}. The other half is covered in two equal time intervals with speeds 9 m/s\mathrm{m} / \mathrm{s} and 15 m/s15 \mathrm{~m} / \mathrm{s} respectively. The average speed of the particle during the motion is :

  1. Option A:

    8.8 m/s8.8 \mathrm{~m} / \mathrm{s}

  2. Option B:

    10 m/s10 \mathrm{~m} / \mathrm{s}

  3. Option C:

    9.2 m/s9.2 \mathrm{~m} / \mathrm{s}

  4. Option D:

    8 m/s8 \mathrm{~m} / \mathrm{s}

    Correct

Answer: D

Step-by-step solution

BD⇒S=9t+15t=24t\mathrm{BD} \Rightarrow \mathrm{S}=9 \mathrm{t}+15 \mathrm{t}=24 \mathrm{t}

AB⇒S=6t1=24t⇒t1=4t\mathrm{AB} \Rightarrow \mathrm{S}=6 \mathrm{t}_{1}=24 \mathrm{t} \Rightarrow \mathrm{t}_{1}=4 \mathrm{t}

<< speed >= dist.  time =48t2t+t1>=\frac{\text { dist. }}{\text { time }}=\frac{48 t}{2 t+t_{1}}

=48t2t+4t⇒48t6t⇒8 m/s=\frac{48 \mathrm{t}}{2 \mathrm{t}+4 \mathrm{t}} \Rightarrow \frac{48 \mathrm{t}}{6 \mathrm{t}} \Rightarrow 8 \mathrm{~m} / \mathrm{s}

Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
9 April, Shift 1
Subject
Physics
Chapter
Motion in one Dimension
Topic
Uniformly Accelerated Motion
A particle moving in a straight line covers half the distance with… | JEE Main 2024 PYQ with Solution · DhiX AI