A race driver has a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.5 m/s^2; after 3.6 s he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of 71.7 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?
Vo = at = 5.5*3.6 = 19.8 m/s.
19.8*t + 0.5*5.5*t^2 = 71.7t,
2.75t^2 + 19.8t - 71.7t = 0,
2.75t^2 - 49.15t = 0.
Use Quadratic Formula and get:
17.9 s.
To solve this problem, we can use the equations of motion. Let's go step by step to find the time required for the entering car to catch up with the other car.
Step 1: Find the initial velocity of the entering car.
The entering car starts from rest, so its initial velocity (u) is 0 m/s.
Step 2: Find the distance traveled by the entering car before entering the main speedway.
We know the acceleration (a) of the entering car is 5.5 m/s^2, and the time (t) taken to enter the main speedway is 3.6 s. We can use the equation of motion:
Distance (s) = ut + (1/2)at^2
Substituting the values, we have:
s = 0 + (1/2)(5.5)(3.6^2)
s = 0 + (1/2)(5.5)(12.96)
s = 0 + 35.76
s = 35.76 m
Step 3: Find the relative velocity between the entering car and the other car.
The relative velocity (v_rel) is the difference between their velocities. The velocity of the other car is given as 71.7 m/s.
v_rel = v_other - v_entering
v_rel = 71.7 - 0
v_rel = 71.7 m/s
Step 4: Find the time required for the entering car to catch up with the other car.
To find the time, we can use the equation of motion:
s = v_rel * t
Substituting the values, we have:
35.76 = 71.7 * t
Dividing both sides of the equation by 71.7, we get:
t = 35.76 / 71.7
t ≈ 0.498 seconds
Therefore, it takes approximately 0.498 seconds for the entering car to catch up with the other car.