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## Homework Statement

(3) A motorist is approaching a green traffic light with speed [itex]v_0[/itex] when the light turns

to amber.

(a) If his reaction time is [itex]\tau[/itex], during which he makes his decision to stop and applies his foot to the

brake, and if the maximum braking deceleration is a, what is the minimum distance [itex]s_{min}[/itex] from the

intersection at the moment the light turns to amber in which he can bring his car to a stop?

(b) If the amber light remains on for a time t before turning red, what is the maximum distance

[itex]s_{max}[/itex] from the intersection at the moment the light turns to amber such that he can continue into the

intersection at speed [itex]v_0[/itex] without running the red light?

(c) Show that if his initial speed [itex]v_0[/itex] is greater than

[itex]v_{0_{max}} = 2a(t- \tau )[/itex]

there will be a range of distance from the intersection such that he can neither stop in time nor

continue through the intersection without running the red light.

## Homework Equations

kinematics equations

## The Attempt at a Solution

A using [itex]vf^2=v_0^2 +2(-a)d[/itex] is [itex] s_{min}=\frac{v_0^2}{2a} +v_0\tau[/itex]

B is simply [itex]v_0 t[/itex]

C i'm almost clueless. i can sub the given expression into both of my derived equations for [itex]s_{min}[/itex] and [itex]s_{max}[/itex] and all i get is that they both equal [itex]2at(t-\tau)[/itex] which i can't see how to use to prove that [itex] s_{max}<s<s_{min}[/itex].

This is actually an intermediate mechanics question but seems simple enough.