You are arguing over a cell phone while trailing an unmarked police car by 30 m.

Question

You are arguing over a cell phone while trailing an unmarked police car by 30 m. Both your car and the police car are traveling at 100 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 emergency braking at 5 m/s2.

b) Suppose that you take another 0.4 s to realize your danger and begin braking. If you too brake at 5 m/s2, what is your speed when you hit the police car?

Explanation / Answer

(a)

105 km/h = 105*103 / (60*60) = 29.17 m/s

the distance the police car traveled in 2 s after brake

S1 = vt - 1/2 at2

my car traveled in 2 s

S2 = vt

separation between the two car after 2 s

= 26 - (S2-S1) = 26 - (1/2)*5*22 = 16 m

(b)

S1 = vt - 1/2 at2

S2 = v(t) - 1/2a(t-2.4)2

when S2-S1 = 26, my car hits police car

solve for t, t = 3.37 s

v = v0 - a (t-2.4) = 29.17 - 5(3.37-2.4) = 24.3 m/s

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