You are arguing over a cell phone while trailing an unmarked policecar by 35 m.

Question

You are arguing over a cell phone while trailing an unmarked policecar by 35 m. Both your car and the policecar are traveling at 110 km/h. Yourargument diverts your attention from the police car for2.5 s (long enough for you to look at thephone and yell, "I won't do that!"). At the beginning of that 2.5s, the police officer begins emergency braking at 5m/s2. (a) What is the separation between the two carswhen your attention finally returns?
1 m

(b) Suppose that you take another 0.4 s to realize your danger andbegin braking. If you too brake at 5 m/s2, what is yourspeed when you hit the police car?
2 km/h
(a) What is the separation between the two carswhen your attention finally returns?
1 m

(b) Suppose that you take another 0.4 s to realize your danger andbegin braking. If you too brake at 5 m/s2, what is yourspeed when you hit the police car?
2 km/h

Explanation / Answer

a)      let the intial velocity of the policecar be = u     in the period of decelerating fora time ' t ' , the distance travelled by the police car= d                  d = ut - at^2 /2      a = breaking decelleration      t = time of breaking if S be the distance travelled by you in the sametime               S = u * t         the gap between youand police car when u pay attention                         = S-d .     now the seperation between your carand police car = 35m-(S-d) b) total time to pay attention = t + 0.4sec .             distacne travelled in t +0.4 sec by your car                S' = v *( t + 0.4sec)          and theseperation                           = 35m-(S'-d)          to hit thecar the seperation between the police car and your car must =0                           35m = S'-d solving for time in the above equaion , and finalvelocity just before to hit the car                           v = u -at t = time of breaking .       if the brakes are applied for0.4 sec the final velociyt of the car in the                                                                                         

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