Two cars `C_(1)` and `C_(2)` moving in the same direction on a straight single lane road with velocities `v_(1)=12 m s^(-1)` and `v_(2) =10 m s^(-1)`, respectively . When the separation between the two was `d=200 m`, `C_(2)` started accelerating to avoid collision. What is the minimum acceleration of car `C_(2)` so that they do not collide?
.

Explanation

By relative
` veca _(C_1 C_2) = veca_(C_1) - veca_(C_2) =0 -a =(-a)`
` vecV_(C_1C_2) = vecV_(c_1) - vecV_(c_2) = 12 - 10 =2 m//s `
so by relativity we want the car to stop .
` therefore V^2 - u^2 = 2as `
`implies 0-2^2 =- 2 xx a xx 200`
`implies a =1/100 m//s ^2 = 0.1 m//s^2 = 1 cm //s^2`
` therefore ` Minimum acceeleration needed by car `C_2 =1 cm //s^2`