Question

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

How long after Car B started the race will Car B catch up with Car A?

Answer 1

Answer:$\frac{D_A}{v_B-v_A}$

Explanation:

Given

car A had a head start of $D_A$

and it starts at x=0 and t=0

Car B has to travel a distance of $D_A and d_a$

where $d_a$ is the distance travel by car A in time t

distance travel by car A is

$d_a=v_A\times t$

For car B with  speed $v_B$

$d_B=D_A+d_a$

$v_B\times t=D_A+v_A\times t$

$t=\frac{D_A}{v_B-v_A}$