A race driver has made a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.4 m/s2; after 4.4 s he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of 68.1 m/s overtakes and passes the entering car. The entering car maintains its acceleration. How much time is required for the entering car to catch up with the other car?

Question

A race driver has made a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.4 m/s2; after 4.4 s he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of 68.1 m/s overtakes and passes the entering car. The entering car maintains its acceleration. How much time is required for the entering car to catch up with the other car?

Answer 1

find the velocity of the first car at 4.4 seconds.

AT that point, both have the same starting point, one is accelerating, one is const velocity. When they meet again, they have traveled the same distance.

d1=vi*t+1/2 a t^2
d2=68.1*t
d1=d2, set them equal, solve for time.

Answer 2

To solve this problem, we can use the equation of motion for the entering car:

v = u + at

where:
- v is the final velocity of the entering car
- u is the initial velocity of the entering car (which is 0 here since it starts from rest)
- a is the acceleration of the entering car (5.4 m/s^2)
- t is the time taken

Since we are trying to find the time it takes for the entering car to catch up with the other car, we need to find the time when their positions are equal.

Let's assume that the distance traveled by the entering car to reach the main speedway is D. Then, the distance traveled by the other car in the same time is also D, as they meet at the same point.

The equation for distance traveled is:
D = ut + (1/2)at^2

Since the initial velocity of the entering car, u, is 0, the equation simplifies to:
D = (1/2)at^2

Now, let's calculate the time it takes for the entering car to reach the main speedway.

Plugging in the values, we get:
D = (1/2)(5.4 m/s^2)(4.4 s)^2

Simplifying, we find:
D = 53.424 m

Now that we know the distance traveled by both cars when they meet, we can find the time it takes for the entering car to catch up with the other car.

The equation for distance traveled is:
D = vt

where v is the velocity of the entering car.

Plugging in the values, we get:
53.424 m = (5.4 m/s)(t)

Simplifying, we find:
t ≈ 9.89 s

Therefore, it will take approximately 9.89 seconds for the entering car to catch up with the other car.