- #1
ice109
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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.