Overcoming a Head Start Part A Cars A and B are racing each other along the same
ID: 1327860 • Letter: O
Question
Overcoming a Head Start Part A 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 Express the time in terms of given quantities. the starting line at t = 0. The starting line is at z = 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. Part A How long after Car B started the race will Car B catch up with Car A? Part B 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.)Explanation / Answer
This can be done by considering the relative velocities.
Apply a negative velocity – Va to both simultaneously so that
A comes to stop and B moves with a speed of (Vb – Va).
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The distance to reach A by B is Da.
The time = (distance /velocity) = Da / (Vb – Va).
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Distance traveled by B in time t {= Da / (Vb – Va)} is
d = velocity x time = Vb* Da / (Vb – VA)}.
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