Problem: Cars A and B are racing each other along the same straight road in the

Question

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?

Express the time in terms of given quantities.

tcatch=

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.)

dpass=

Please write out each step with explanation. Thank you so much

Explanation / Answer

1) suppose after time t, Car B catches Car A.

DIstance traveled by A in this time, dA = vA t

by Car B:

suppose acc of car B is a then it wil accelerate until its speed becoems vB.

tcatch = t'

then a = vB / t'

distance traveled in t' = (vB / t') (t'^2) / 2 = vB t' / 2

distace traveled in (t -t') time = vB (t - t')

= vB t - vB t'

dB = vBt - vB t' + vB t'/2

dB = vB t - vB t' /2

and dA = dB

vA t = vB t - vB t' /2

t = vB tcatch / (2(vB - vA) )

(2) d = vA t = vA vB tcatch / (2 (vB - vA))

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