Question

You are arguing over a cell phone while trailing an unmarked police car by 25 m; both your car and the police car are traveling at 110 km/h. Your argument diverts your attention from the police car for 2.0 s (long enough for you to look at the phone and yell, "I won’t do that!"). At the beginning of that 2.0 s, the police officer begins braking suddenly at 5.0 m/s². If you too brake at 5.0 m/s², what is your speed when you hit the police car? a) 110km/h

b) 25m/s
c) 15m/s
d) 35m/s

Answer 1

Your speed when you hit the police car is approximately 35 m/s.

Step-by-step explanation:

To determine your speed when you hit the police car, we need to calculate the time it takes for both you and the police car to come to a stop. Since you are trailing the police car by 25 m, we can first find the time it takes for the police car to stop using the equation:

Δv = at

where Δv is the change in velocity, a is the acceleration, and t is the time taken. Plugging in the values, we get:

5 m/s² = (110 km/h) / t

solving for t, the time it takes for the police car to stop is 11 s. Since you were distracted for 2.0 s, your time taken is 9.0 s. Now, we can find your final speed using the equation:

v = vo + at

where v is the final velocity, vo is the initial velocity, a is the acceleration, and t is the time. Plugging in the values, we get:

v = (110 km/h) - (5 m/s²)(9.0 s)

converting km/h to m/s, the final speed when you hit the police car is approximately 35 m/s.