“VisionZero” is an organization that wants to reduce car fatalities in the Bay A

Question

“VisionZero” is an organization that wants to reduce car fatalities in the Bay Area tozero. One of their radio commercials state that increasing your speed by 10 miles perhour (4.5 m/s) doubles the amount of distance that it takes to stop.
(a) (2 points) Assuming a car of mass m, and a coecient of friction µ, and an initialspeed v0, nd the stopping distance d. (Assume the road is horizontal).

(b) (3 points) It is not true for every speed that increasing the speed by 10 miles perhour doubles d. Take m = 2000 kg, g = 9.8 m/s2, µ = 0.65. Find the speed v0 thatVisionZero is assuming (i.e. nd the speed v0 that has v0 + 10 mph has twice the

stopping distance)

Explanation / Answer

a)

Vo = initial speed

d = stopping distance

Vf = final speed = 0

a = acceleration = - µg

using the kinematics equation

Vf2 = Vo2 + 2 a d

02 = Vo2 + 2 (- µg ) d

d = Vo2 /(2µg)

b)

10 mph = 4.47 m/s

Vo' = Vo + 4.47

d' = stopping distance = 2 d = 2Vo2 /(2µg) = Vo2 /(µg)

Vf = final speed = 0

a = acceleration = - µg

using the kinematics equation

V'f2 = V'o2 + 2 a d'

02 = (Vo + 4.47)2 + 2 (- µg ) (Vo2 /(µg))

02 = (Vo + 4.47)2 + 2 (- 1 ) (Vo2 )

Vo = 10.8 m/s = 24.2 mph

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