Question

Two car travelling towards each other on a straight road at velocity $10\text{m/sec}$ and $12\text{m/sec}$ respectively. When they are $150\text{m}$ apart, both drivers apply their brakes and each car decelerates at $2\text{m}/{\text{sec}}^2$ until it stops. How far apart will they be when they have both come to a stop ?

Answer 1

Given: $u_A=10\text{m/s},u_B=12\text{m/s},a=2\text{m/}{\text{s}}^2,d=150\text{m}$

The distance travelled by car A , when it stops,

$S_A=\frac{u_A^2}{2a}=\frac{{10}^2}{2\times 2}=25\text{m}$

The distance travelled by car $B$ , when it stops,

$S_A=\frac{u_B^2}{2a}=\frac{{12}^2}{2\times 2}=36\text{m}$

$\therefore$ Minimum distance between the cars when both are stop is $150-(25+36)=89\text{m}$

Hence, option $B$ is correct.