A motorist is approaching a traffic light with speed v0 when the light turns gre

Question

A motorist is approaching a traffic light with speed v0 when the light turns green to amber. His distance to the light at this moment is x. His reaction time is t0 and his maximum negative acceleration is a. What is the minimum distance x in which the motorist can stop without passing the light? If the light remains amber for t1 and he continues at v0, what is the maximum distance x the motorist can be from the light and pass through the light before it turns red. For what value of v0 must the motorist pass through a red light? Express your answer in terms of a, t0, t1. (In this situation, there exists a range of x which, if the motorist is in that range when the light turns amber, he will always end up running the red light.)

Explanation / Answer

1) Distance that will be traveled before braking = Vo t

Distance that will be traveled while braking = Vo t - (1/2)aT^2
or alternately: using: V^2 = Vo^2 - 2ad
Substituting: 0 = Vo^2 - 2ad (because final velocity is 0)
d = (1/2)Vo^2/a

Total minimum distance to stop is thus: Vot + (Vo^2)/(2a)

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