Car A is 12 m ahead of car B on a straight stretch of road. Car A starts from rest and accelerates away from B at 4.0 m/s2. Two seconds later B starts from rest and accelerates after A at 6.0 m/s2. How long will it take B to catch A? How far will B have travelled?

Question

Car A is 12 m ahead of car B on a straight stretch of road. Car A starts from rest and accelerates away from B at 4.0 m/s2. Two seconds later B starts from rest and accelerates after A at 6.0 m/s2. How long will it take B to catch A? How far will B have travelled?

Answer 1

B travels distanceA + 12

B=1/2 6 *(t-2)^2
A-1/2 4 *t^2
B+12=A
put A, B in that, solve for t
B's time is t-2
How far, solve for B

Answer 2

Are u dumb? How is B+12 = A? if A is 12 m AHEAD of B, then how tf A go LONGER THAN B?

Answer 3

So Ur saying that A-12 = B, which means that A must go a longer distance than B to get a positive number. YET IF A IS AHEAD, THAT MEANS IT WENT A SHORTER DISTANCE THAN B. Stop posting the wrong answer for people to fail their physics tests

Answer 4

To find out how long it will take car B to catch up to car A, we need to determine the time it will take for both cars to cover the same distance.

First, let's find the time it takes for car A to cover the distance between them. We know that car A starts from rest and accelerates at 4.0 m/s^2. We can use the equation of motion:

s = ut + (1/2)at^2

where:
- s is the distance covered,
- u is the initial velocity (0 m/s for car A),
- t is the time elapsed,
- a is the acceleration (4.0 m/s^2 for car A).

Since we want to find the time it takes for car A to cover the distance, we can rearrange the equation as:

t = sqrt(2s/a)

Substituting the given values, we have:

t = sqrt(2 * 12 m / 4.0 m/s^2)
t = sqrt(6)
t ≈ 2.45 seconds

So, it will take car A approximately 2.45 seconds to cover the distance between them.

Now, let's find out how far car B will have travelled in that same period of time. Car B starts 2 seconds after car A and has an acceleration of 6.0 m/s^2. Using the same equation of motion, we can find the distance covered by car B:

s = ut + (1/2)at^2

Since car A has already covered 12 meters in the time it takes for car B to catch up, the distance covered by car B will be:

s = ut + (1/2)at^2
s = 0 + (1/2) * 6.0 m/s^2 * (2.45 s)^2
s ≈ 14.72 meters

Therefore, car B will have traveled approximately 14.72 meters when it catches up to car A.