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.

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?
Express the time in terms of given quantities.

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.)

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3 answers
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Answer 1

bobpursley answered
10 years ago

ok, when they meet.

finalpositionB=x =vB*time
final poistionA=x+DB=vA*time+DB

setting these final positions equal
vA*time+DB=vB*time
time=DB/(vB-Va)

Answer 2

Step-by-Step Bot answered
1 year ago

To determine the time it takes for Car B to catch up with Car A, we can set up a basic equation.

Let t be the time after Car B started the race.

Car A would have traveled a distance of DA + vA * t.
Car B, on the other hand, would have traveled a distance of vB * t (since Car B has a head start of 0).

For Car B to catch up with Car A, the distances traveled by both cars must be equal. Therefore, we can set up the equation:

DA + vA * t = vB * t

Now, let's solve for t:

DA = vB * t - vA * t
DA = (vB - vA) * t
t = DA / (vB - vA)

So, the time it takes for Car B to catch up with Car A is t = DA / (vB - vA).

To determine the distance from Car B's starting line when Car B passes Car A, we can substitute the value of t into either Car A's or Car B's distance equation.

Let's substitute it into Car B's equation:

Distance from Car B's starting line = vB * t

Substituting t = DA / (vB - vA):

Distance from Car B's starting line = vB * (DA / (vB - vA))

Therefore, the cars will be a distance of vB * (DA / (vB - vA)) from Car B's starting line when Car B passes Car A.

Answer 3

Explain Bot answered
1 year ago

To find the time it takes for Car B to catch up with Car A, we can set up an equation using the distance traveled by each car.

Let's say the time it takes for Car B to catch up with Car A is tcatch.

Car A travels at a constant speed vA, so the distance it travels in tcatch time is DA + vA * tcatch.

Car B starts at x = 0, so the distance it travels in tcatch time is vB * tcatch.

To find the time tcatch, we can equate these two distances:

DA + vA * tcatch = vB * tcatch

Now, let's solve for tcatch:

DA = tcatch(vB - vA)
tcatch = DA / (vB - vA)

So, the time it takes for Car B to catch up with Car A is tcatch = DA / (vB - vA).

To find the distance from Car B's starting line when Car B passes Car A, we can substitute the value of tcatch into either of the distance equations.

Let's use the distance equation for Car B:

Distance from Car B's starting line = vB * tcatch

Substituting the value of tcatch, we get:

Distance from Car B's starting line = vB * (DA / (vB - vA))

Therefore, the distance from Car B's starting line when Car B passes Car A is vB * (DA / (vB - vA)).