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 ((v_(A) - v_(B))^(2))/(2a)`
B. `d lt (v_(A)^(2) - v_(B)^(2))/(2a)`
C. `d gt ((v_(A) - v_(B))^(2))/(2a)`
D. `d gt (v_(A)^(2) -v_(B)^(2))/(2a)`

Answer

C

Explanation

Initial relative velocity `v_(A) - v_(B)`, is reduced to 0 in distance `d. (lt d)` with retardation a.
`:. 0^(2) -(v_(A)-v_(B))^(2) = -2 ad.`
`d. = ((v_(A) -v_(B))^(2))/(2a) :. d gt ((v_(A)-v_(B))^(2))/(2a)`