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

Question

While driving your car you suddenly see a state trooper ahead of you. At that instant, your speed is 65 mi/hr. You want to bring your car under the 45 mi/hr speed limit as quickly as possible. You recall that your car's brakes decelerate at 4.3 m/s2.

Suppose that when you engage your brakes, they do not instantly achieve their maximum acceleration magnitude. Instead, suppose that it takes 0.2 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.

Explanation / Answer

given that

a = 4.3m/s2

t = 0.2 s

to = 0

vo = 45 mi/hr = 20.11 m/s

ao = a/t =4.3/0.2 = 21.5 m/s2

considering formula

d(t) = vo(t - to) +t*ao [t2/2 - to2/2] - ao/3 [t3 - to3]

d(t) = 20.11* (0.2) + 0.2*21.5[0.22/2] - 21.5/3[0.23]

d(t) = 4.16 m

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