# Kinematics of Traffic Congestion

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This simple model of traffic congestion on an expressway calculates the optimum speed for a given flow of vehicles. First the model calculates the stopping distance , which is the sum of the length of the car , the distance that the car moves while the driver reacts , and the braking distance based on the deceleration.

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Contributed by: Enrique Zeleny (March 2011)

Open content licensed under CC BY-NC-SA

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## Details

We are using basic formulas of kinematics , where is the initial velocity, and . The capacity is defined as , where is the number of cars and is the stopping time. On the other hand, . It can be shown that , which is the function plotted.

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