Question

How long after Car B started the race wil Car B catch up with Car A? Express the time in terms of given quantities. Review 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 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 vp, which is greater than vA View Available Hint(s) catch Submit ▼ 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.) View Available Hint(s)

Answer 1

Part A.

Given that Initial distance between Car A and Car B is D_A, (where Car A is ahead of car B) And

Car A is moving at a constant speed of v_A

Car B is moving at a constant speed of v_B

Now at the moment when car B catches car A, then

distance traveled by car = distance between car A and Car B + distance traveled by car A

d_B = D_A + d_A

Now we know that distance = Speed*time, Suppose car B catch car A in 't_catch' time, then in this time

d_B = v_B*t_catch

d_A = v_A*t_catch

So,

v_B*t_catch = D_A + v_A*t_catch

t_catch*(v_B - v_A) = D_A

t_catch = D_A/(v_B - v_A)

$\mathbf{t_{catch} = \frac{D_A}{v_B - v_A}}$

Part B.

when the car B passes car A, then distance from Car B's starting line will be d_B, So from above we know that

d_B = v_B*t_catch

d_B = v_B*D_A/(v_B - v_A)

dg = VB*DA VB – VA