Question

A police car waits in hiding slightly off the highway. A speeding car is spotted by the police car doing 40 m/s. At the instant the speeding car passes the police car, the police car accelerates from rest at 4 m/s² to catch the speeding car. How long does it take the police car to catch the speeding car?

a) 10 s
b) 12.5 s
c) 15 s
d) 20 s

Answer 1

By setting the displacement equations of both the police car and the speeding car equal to each other, we can find that it takes 20 seconds for the police car to catch the speeding car.

Step-by-step explanation:

To figure out how long it will take the police car to catch up to the speeding car, we must first note that the speeding car has a constant velocity, and the police car starts from rest but has an acceleration. For the police car, the equation for displacement starting from rest is given by x = 1/2 at², where a is acceleration and t is the time. Since the speeding car has a constant velocity, its displacement is given by x = vt, where v is velocity and t is time. Next, set these two equations equal to each other since both vehicles will have traveled the same displacement when the police car catches up.

x = vt = 1/2 at²
Insert the given values for v (40 m/s) and a (4 m/s²) to find the time t.
40t = 1/2 * 4 * t²
Which simplifies to:
t² - 20t = 0
You can factor this quadratic equation as:
t(t - 20) = 0
So, t = 0 or t = 20 seconds. Since we're looking for the time after the chase begins, we discard t = 0 and conclude that it takes 20 seconds for the police car to catch the speeding car.