Two cars `A` and `B` of equal masses `(100 Kg)` are moving on a straight horizontal road with same velocity `3m//s` as shown. At `t = 0` car A starts accelerating with constant acceleration of `2 m//s^(2)` (intial separation between car is `25 m`). Choose correct options (neglect length of cars)

Options

A. car `A` catches car `B` at `t = 6` sec.
B. magnitude of displacment of car `B w.r.t` car `A` is first `2` sec.
C. car `A` will catch car `B` at `t = 5` sec.
D. magnitude of displacement of car `B w.r.t.` car `A` is `4 m` in first `2` sec

Answer

C, D

Explanation

`w.r.t B, a_(rel) = 2m//s^(2), u_(rel) = 0`.
`s_(rel) = 25`
`rArr 25 = (1)/(2) xx 2 xx t^(2) rArr t = 5 sec`
`S_(BA)(2) = 0 + (1)/(2) xx 2 xx 2^(2)`
`= 4 m`