You are arguing over a cell phone while trailing an unmarked police car by 26.0

Question

You are arguing over a cell phone while trailing an unmarked police car by 26.0 m; both your car and the police car are traveling at 120 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 5.05 m/s2. (a) What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.400 s to realize your danger and begin braking. (b) If you too brake at 5.05 m/s2, what is your speed when you hit the police car?

Explanation / Answer

120000m/h = 53.64meters sec

distance between = 26 - 1/2 (5.05) t^2
at 2 seconds distance = 26 -0.5(5.05) 2^2
= 15.9 meters

distance when you begin braking
distance = 26 -0.5(5.05) 2.4^2
= 11.45 meters
police car speed when you begin braking
v= 53.64 -5.05 (2.4)
=41.52m/s
distance during braking
d = 11.45 - (53.64-11.45)t - 0.5 (5.05-5.05)t^2

= 42.41t -
time to impact
0 = 11.45- 42.41t
t= 11.45/42.41 sec= .2699 sec past the 2.4 seconds

police car speed at 2.4 + .269 sec

v= 53.64 - ( 2.669)5.05
v= 40.05 m/s

your speed 53.64 -(.269) 5.05
= 52.28 m/s

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