Two cars are travelling towards each other at speed of 20 ~m ~s^ -1 each. When the cars are 300 ~m apart, both the drivers apply brakes and the cars retard at the rate of 2 ~m ~s^ -2 . The distance between them when

Correct answer: B. 100 ~m aligned & | u_ BA |=40 m / s & | a_ BA |=4 m / s & Apply (v^2=u^2+2 as)_ relative & O=(40)^2+2(-4)(S) & S=200 m & Remaining distance =300-200=100 m aligned

JEE Main 20249 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 9 April
Shift: Evening Shift
Subject: Physics
Chapter: Motion in One Dimension

JEE Main 2024 · 9 April · Evening Shift · Physics · Motion in One Dimension

Two cars are travelling towards each other at speed of 20 ~m ~s^ -1...

Two cars are travelling towards each other at speed of

20 \mathrm{~m} \mathrm{~s}^{-1}

each. When the cars are

300 \mathrm{~m}

apart, both the drivers apply brakes and the cars retard at the rate of

2 \mathrm{~m} \mathrm{~s}^{-2}

. The distance between them when they come to rest is :

Options

A $200 \mathrm{~m}$
B $100 \mathrm{~m}$
C $50 \mathrm{~m}$
D $25 \mathrm{~m}$

Correct answer

B. $100 \mathrm{~m}$

Step-by-step solution

\begin{aligned} & \left|\overrightarrow{\mathrm{u}_{\mathrm{BA}}\right|=40 \mathrm{ m} / \mathrm{s} \\ & \left|\overrightarrow{\mathrm{a}_{\mathrm{BA}}\right|=4 \mathrm{ m} / \mathrm{s} \\ & \text{ Apply }\left(\mathrm{v}^2=\mathrm{u}^2+2 \mathrm{as}\right)_{\text{relative }} \\ & \mathrm{O}=(40)^2+2(-4)(\mathrm{S}) \\ & \mathrm{S}=200 \mathrm{ m} \\ & \text{ Remaining distance }=300-200=100 \mathrm{ m}\end{aligned}

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