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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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