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. `d lt ((upsilon_(1)-upsilon_(2))^(2))/(2a)`
B. `d lt (upsilon_(1)^(2)-upsilon_(2)^(2))/(2a)`
C. `d gt ((upsilon_(1)-upsilon_(2))^(2))/(2a)`
D. `d gt (upsilon_(1)^(2)-upsilon_(2)^(2))/(2a)`

Answer

C

Explanation

Initial relative velocity `= upsilon_(1)-upsilon_(2)`, Final relative velocity = 0
From `upsilon^(2)=u^(2)-2as rArr 0 = (upsilon_(1)-upsilon_(2))^(2)-2xxaxxs`
`rArr s=((upsilon_(1)-upsilon_(2))^(2))/(2a)`
If the distance between two cars is s, then collision will take placed. To avoid collision `d gt s`
`therefore d gt ((upsilon_(1)-upsilon_(2))^(2))/(2a)`
where, d = actual initial distance between two cars.