Two cars are travelling towards each other on a straight road with velocities `10 m s^(-1) and 12 m s^(-1)` respectively. When they are 150 m apart, both drivers apply their brakes and each car decelerates at `2 m s^(-2)` until it stops. How far apart will they be when they have come to rest?

Explanation

Let `x_(1)` and `x_(2)` be the distance travelled by the car before they stop under deceleration. From IIIrd equation of motion
`v^(2)=u^(2)+2as`
`rArr 0=(10)^(2)-2xx2x_(1) rArr x_(1)=25 m`
and `0 = (12)^(2) - 2xx2x_(2) rArr x_(2)=36 m`
Total distance covered by the two cars
`x_(1)+x_(2)=25+36=61 m`
Distance between the two cars when they stop
`=150-61=89 m`