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.

Question

How long after Car B started the race will Car B catch up with Car A?
Express the time in terms of given quantities.

How far from Car B's starting line will the cars be when Car B passes Car A?
Express your answer in terms of known quantities. (You may use tcatch as well.)

Answer 1

ok, when they meet.
finalpositionB=x =vB*time
final poistionA=x+DB=vA*time+DB

setting these final positions equal
vA*time+DB=vB*time
time=DB/(vB-Va)