Catch/Overtake Problems Video Lessons

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Problem: 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? 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 tcatch as well.)

FREE Expert Solution

The cars move with constant velocity. Thus we do not need to use the UAM equations. 

Distance, velocity, and time are related by:

x=v·t

(1)

The position equations for the motions are:

xA = vAt + DA 

xB = vB

When the two cars catch up, 

xA = xB

vAt + DA =  vB

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Problem Details

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? 

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 tcatch as well.)

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What scientific concept do you need to know in order to solve this problem?

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Based on our data, we think this problem is relevant for Professor Hodby's class at UCB.