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 ​

Question

Two cars are travelling towards each other at speed of 20 m \(\text{s}^{–1}\) each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m \(\text{s}^{–2}\) . The distance between them when they come to rest is : 

(1) 200 m 

(2) 50 m 

(3) 100 m 

(4) 25 m 

Answer 1

Correct option is :  (3) 100 m  

\(\left|\overrightarrow{\mathrm{u}}_{\mathrm{BA}}\right|=40 \mathrm{~m} / \mathrm{s}\)

\(\left|\overrightarrow{\mathrm{a}}_{\mathrm{BA}}\right|=4 \mathrm{~m} / \mathrm{s}\)

Apply \(\left(\mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}\right)_{\text {relative }}\)

\(\mathrm{O}=(40)^{2}+2(-4)(\mathrm{S})\)

\(\mathrm{S}=200 \mathrm{~m}\)

Remaining distance \(=300-200=100 \mathrm{~m}\)