The cars move with constant velocity. Thus we **do not** need to use the UAM equations.

Distance, velocity, and time are related by:

$\overline{){\mathbf{x}}{\mathbf{=}}{\mathbf{v}}{\mathbf{\xb7}}{\mathbf{t}}}$

**(1)**

The position equations for the motions are:

x_{A} = v_{A}t + D_{A}

x_{B} = v_{B}t

When the two cars catch up,

x_{A} = x_{B}

v_{A}t + D_{A} = v_{B}t

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 D_{A} beyond the starting line at t = 0. The starting line is at x = 0. Car A travels at a constant speed v_{A}. Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed v_{B}, which is greater than v_{A}.

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 t_{catch} as well.)

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Catch/Overtake Problems concept. You can view video lessons to learn Catch/Overtake Problems. Or if you need more Catch/Overtake Problems practice, you can also practice Catch/Overtake Problems practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Hodby's class at UCB.