You are arguing over a cell phone while trailing an unmarked police car by 36 m.
ID: 1406785 • Letter: Y
Question
You are arguing over a cell phone while trailing an unmarked police car by 36 m. Both your car and the police car are traveling at 100 km/h. Your argument diverts your attention from the police car for 2.5 s (long enough for you to look at the phone and yell, "I won't do that!"). At the beginning of that 2.5 s, the police officer begins emergency braking at 5 m/s2.
(a) What is the separation between the two cars when your attention finally returns?
(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
Initial speed of the cars v = 100 km / h
= 100 x 1000 m / 3600 s
= 27.777 m / s
Initial separaton of police car and your car = 36 m
Distance travel by your car in 2.5 s is S = velocity of car x time
= 27.777 x 2.5
= 69.4444 m
accleration of the police car a = -5 m/s 2
Distance travel by police car in 2.5 s after braking is S ' = vt + ( 1/ 2) at 2
= 69.444 - 15.625 m
= 53.819 m
Separation of the police car and your car after 2.5 s is = ( 36 + S ' ) - S
= 20.375 m
(b).Realizing time t ' = 0.4 s
Let the Time taken to stop the the police car be T .
i.e., final velocity of the police car V = 0
From the relation V = v + aT
T = ( V - v) / a
= 5.5554 s
Total time to realize for braking is t " = T - ( 2.5 s + 0.4 s )
= 2.6554 s
Speed of your car after time t " and braking is V ' = v + at "
= 27.777+ ( -5) 2.6554
= 27.777 - 13.277
= 14.5 m/ s
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