4) While driving your car you suddenly see a state trooper ahead of you. At that

Question

4) While driving your car you suddenly see a state trooper ahead of you. At that instant, your speed is 68 mi/hr. You want to bring your car under the 50 mi/hr speed limit as quickly as possible. You recall that your cars brakes decelerate at 4.5 m/s2. How long does it take you to slow down to an acceptable speed? 15) How far do you travel while slowing down? 16) Suppose that when you engage your brakes, they do not instantly achieve their maximum acceleration magnitude. Instead, suppose that it takes O.1 seconds to reach maximum braking acceleration. How much farther do you travel as a result of this delay? Assume that the braking acceleration increases linearly until it reaches its maximum magnitude Answer:

Explanation / Answer

initial speed =v0= 68 miles / hour = 30.398 m/sec

final speed = vf = 50 miles/hr = 22.35 m/sec

deceleration = a = - 4.5 m/sec^2

vf = v0 + a t

time = t = vf - v0 / a = 22.35 - 30.4 / -4.5 = 1.79 sec

b) vf^2 - v0^2 = 2as

distance = s = vf^2 - v0^2 / 2 a = 22.35^2 - 30.4^2 / 2* 4.5 = 47.3 m

c) total time = 1.79 + 0.1 = 1.89 sec

s = v0 *t + 1/2 a t^2 = 30.4* 1.89 - 8.037 = 49.4 m

further distance = 49.4 - 47.3= 2.1 m

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