Rachel and Sarah are on a bus travelling at 5 mph past John who is standing on the sidewalk. Rachel then throws a ball
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The question is incomplete. Here is the complete question.
Cars A nad B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance beyond the starting line at t = 0. The starting line is at x = 0. Car A travels at a constant speed
. Car B starts at the starting line but has a better engine than Car A and thus Car B travels at a constant speed
, which is greater than
.
Part A: How long after Car B started the race will Car B catch up with Car A? Express the time in terms of given quantities.
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.
Answer: Part A:
Part B:
Explanation: First, let's write an equation of motion for each car.
Both cars travels with constant speed. So, they are an uniform rectilinear motion and its position equation is of the form:
where
is initial position
v is velocity
t is time
Car A started the race at a distance. So at t = 0, initial position is .
The equation will be:
Car B started at the starting line. So, its equation is
Part A: When they meet, both car are at "the same position":
Car B meet with Car A after units of time.
Part B: With the meeting time, we can determine the position they will be:
Since Car B started at the starting line, the distance Car B will be when it passes Car A is units of distance.