Question: Object A is moving at a maximum speed of 6m/s towards Object B. At 50 m away Object B accelerates from the approaching Object A at 0.3m/s^2. Does Object A catch up to Object B and if yes when?

Question

I don't know how to answer this at all or even which kinematic equation to use. Maybe distance/velocity=time so it takes i know object A takes 8.3 to reach object B's start point but I don't get it really. Thanks

Answer 1

distance A goes = 50 + distance B goes

6 t = 50 + B
B = (1/2) a t^2 = .15 t^2

so

6 t = 50 + .15 t^2

.15 t^2 - 6 t + 50 = 0

does that have a positive real root?
b^2-4ac = 36 - 30 = 6
sure enough so there is a time when they hit

t = [ 6 +/- sqrt 6 ] /.3

Answer 2

By the way it will happen twice.
The first time is when A catches up with B and is moving faster at 6 m/s
the second time is as A is ahead of B but B is still accelerating and will catch up with A
You want the first time I suspect. so use the - sign answer.