Police Car
How fast is this person going in his car when he hits the police car?
You are arguing over a Cell Phone while trailing an unmarked police car by 25m; both your car and the police car are traveling at 110km/h. Your argument diverts your attention from the police car for 2.0s (long enough for you to look at the phone and yell, “I won’t do that!”). At the beginning of that 2.0s, the police officer begins braking suddenly at 5.0m/s2. (a) What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.40s to realize your danger and begin braking. (b) If you too brake at 5.0 m/s2, what is your speed when you hit the police car?
Initial distance of separation =25m
This distance of separation will be reduced by the amount 0.5 at^2, since both have the same initial speed.
0.5 at^2 = 0.5 x [5] x 2^2 = 10m.
The distance of separation reduces to 25 -10 = 15m
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In 2.4s the distance of separation reduces to
25 – 0.5 x [- 5] x 2 .4^2 = 10.6m
==========================================
After 2.4 second the initial speed of police is
u = 30.6 -5* 2.4 = 18.6m/s
After 2.4 second your initial speed is = 30.6.m/s
Since both have the same deceleration, the time to reduce this distance of separation of 10.6 m/s to zero is given by [distance of separation / difference in speeds].
t = 10.6 / [30.6─18.6]
t = 0.88second
Your velocity at the time of hitting is v = u -at
30.6 – 5 x0.88 = 26.2 m/s
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