# Thread: Physics Average Velocity Problem with People Running/Walking

1. ## Physics Average Velocity Problem with People Running/Walking

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.

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

B. How far from Car B's starting line will the cars be when Car B passes Car A?

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I know that average velocity is equal to (displacement)/(total time). I'm not sure if I can use that to find the unknown time amount of the question.

2. ## Re: Physics Average Velocity Problem with People Running/Walking

Originally Posted by ayyisei
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.

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

B. How far from Car B's starting line will the cars be when Car B passes Car A?

- - - - - - - - - - - - - - - - - - - - - - - - - -

I know that average velocity is equal to (displacement)/(total time). I'm not sure if I can use that to find the unknown time amount of the question.
car "A's" position as a function of time ...

$x_a(t) = d_a + v_a \cdot t$

car "B's" position as a function of time ...

$x_b(t) = v_b \cdot t$

part (A) ... to find the time they are at the same position, set $x_a(t) = x_b(t)$ and solve for $t$

part (B) ... find car "B's" position at the time found in part (A).