Two cars travelling towards each other on a straight road at velocity `10 m//s` and `12 m//s` respectively. When they are 150 metre 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 both come to a stop?

Options

A. 89 m
B. 98 m
C. 108 m
D. 150 m

Answer

A

Explanation

Let `x_(1) and x_(2)` be the distance travelled by the cars before they stop under deceleration.
Using , `v^2 =u^2 +2as ` , we get
` 0 = (10)^2 -2 xx 2xx x_(1) " "...(i)`
`0 = (12)^2 - 2 xx 2 x_(2) " "...(ii)`
Solving eqns. (i) and (ii) , we get
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