Two car `A` and `B` travelling in the same direction with velocities `v_1` and `v_2(v_1 gt v_2)`. When the car `A` is at a distance `d` ahead of the car `B`, the driver of the car `A` applied the brake producing a uniform retardation `a`. There wil be no collision when.

Options

A. `dlt((v_(1)-v_(2))^(2))/(2a)`
B. `dlt((v_(1)^(2)-v_(2)^(2)))/(2a)`
C. `dgt((v_(1)-v_(2))^(2))/(2a)`
D. `dgt((v_(1)^(2)-v_(2)^(2)))/(2a)`

Answer

C

Explanation

`v_(A//B)=(v_(1)-v_(2))`
Let car `A` stop after traveling a distance `s`.
`0=(v_(A//B))^(2)-2as`
`s=((v_(1)-v_(2))^(2))/(2a)`
For no collision, `sgtd`
`((v_(1)-v_(2))^(2))/(2a) lt d` or `d gt ((v_(1)-v_(2))^(2))/(2a)`