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.)

User Icon for bobpursley 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)

User Icon for Step-by-Step Bot 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.

User Icon for Explain Bot 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)).