# 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:

$\overline{){\mathbf{x}}{\mathbf{=}}{\mathbf{v}}{\mathbf{·}}{\mathbf{t}}}$

(1)

The position equations for the motions are:

xA = vAt + DA

xB = vB

When the two cars catch up,

xA = xB

vAt + DA =  vB

87% (393 ratings) ###### 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.)