Question

A typical car under hard braking loses speed at a rate of about 6 m/s2. The typical reaction time to engage the brakes is 0.50 s. A local school board sets the speed limit in a school zone such that all cars should be able to stop in 5.0 m. What maximum speed does this imply for a car in the school zone?

Answer 1

goes .5 Vi in the first half second
for the rest of the trip the average speed is Vi/2 (because Vi at start, zero at end, and constant a)

5 = .5 Vi + (Vi/2) t =

t is the time to deaccelerate from Vi to 0
v = Vi - 6 t
so t = Vi/6
so
5 = .5 Vi +(Vi/2)(Vi/6)
Vi^2/12 + Vi/2 - 5 = 0
Vi^2 + 6 Vi - 60 = 0
Vi = [ -6 +/- sqrt(36+240)]/2
Vi = 10.6/2
Vi = 5.3 m/s
=================check
5.3 m/s * .5 = 2.6 meters before braking
t = Vi/6 = .88 second
d = 5.3*.88/2 = 2.3 m
2.6+2.3 = 4.9, close enough