Question 142 of 308

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 :

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

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Answer: (B) $100 \mathrm{~m}$

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