Physics Homework: How long after Car B started the race will Car B..

Q)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.

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

2) 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 as well).

Sol:

1) Time taken = Distance travelled/Velocity

Distance travelled by Car A = DA

Velocity = Difference in velocity between Car B and Car A

         = VB – VA

Therefore, Time taken t= DA/(VB-VA) secs

2) Distance travelled by Car B in time t= DA/(VB-VA),

S=(Velocity of Car B) *(time taken)

 = VB*DA/(VB-VA) mts