Question

Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance DA beyond the starting line at t=0. The starting line is at x=0. Car A travels at a constant speed vA. Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed vB, which is greater than vA

How long after Car B started the race will Car B catch up with Car A?

Answer 1

Answer:
`(D_A)/(v_B-v_A)`

Step-by-step explanation:

Given

car A had a head start of
`D_A`

and it starts at x=0 and t=0

Car B has to travel a distance of
`D_A and d_a`

where
`d_a` is the distance travel by car A in time t

distance travel by car A is

`d_a=v_A* t`

For car B with speed
`v_B`

`d_B=D_A+d_a`

`v_B* t=D_A+v_A* t`

`t=(D_A)/(v_B-v_A)`