Cars A and B are racing each other along the same straight road in the following
ID: 2286642 • Letter: C
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?
Express the time in terms of given quantities.
tcatch =
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.)
tcatch =
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.)
dpass =Explanation / Answer
so xA = dA + vA t
xB = vB t
we want xB = xA
so v Bt = dA + vA t
(vB - vA) t = dA
t = dA/(vb - va)
b) plug this back into xb
x = vb* dA/(vb - va)