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 5.15 m/s^2. What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.500 s to realize your danger and begin braking. If you too brake at 5.15 m/s^2, what is your speed when you hit the police car?

Explanation / Answer

(a)
Initial Distance btw two cars = 26 m
Speed =120 Km/hr = 33.33 m/s

Distance travelled by you in 2s, = 33.3 * 2= 66.66 m
Distance travelled by Police car in 2 s, S = u*t - 1/2at^2
S = 33.33*2 - 1/2*5.15*2^2
S = 56.36 m

So Final Distance bt You & Police car, = 26m - (66.66 - 56.66)
D =  15.7 m

(b)
Distance btw the two cars after 2.5 s, = 26 - (83.25 - 67.25) = 10 m

Let You crash police car after t seconds.
Distance travelled would have a diffrence of 26 m
Distance travelled by You - Distance travelled by Police car = 26

83.25 + 33.3*t - 1/2*5.15*t^2 - (33.3*(t+2.5)) - 1/2*5.15*(t+2.5)^2) = 26
t = 0.77 s

V = u - a*t
V = 33.3 - 5.15*0.77
V = 29.33 m/s
Speed of your car when you hit the police car, V = 29.33 m/s

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