Final answer:
To calculate when the motorcycle cop catches up to the speeding car, we used kinematic equations, finding that the cop would catch the car in approximately 25.714 seconds.
Step-by-step explanation:
The subject of the question is Physics, specifically involving kinematic equations for motion. The grade level of this question is High School physics. To determine at what time the motorcycle cop catches up to the car, we use the equations of motion for both vehicles, assuming that the cop starts from rest and the car travels at a constant velocity.
For the car with constant velocity (vc = 45 m/s):
Displacement of car (xc) = vc × t
For the motorcycle cop accelerating from rest (amc = 3.5 m/s2):
Displacement of motorcycle cop (xmc) = 0.5 × amc × t2
To catch the car, both vehicles must have traveled the same displacement (xc = xmc).
Solving for time (t) we get:
45t = 0.5 × 3.5 × t2
90t = 3.5 × t2
t2 - (90/3.5) t = 0
t2 - 25.714t = 0
t(t - 25.714) = 0
Ignoring the t = 0 solution (since we are looking for the time after the car passes), we get t = 25.714 seconds. Therefore, it takes approximately 25.714 seconds for the motorcycle cop to catch up to the car.