What are the optimal speed and safe following distance that allow the maximum flow rate (cars per unit time)? The solution to the problem would be useful in controlling trafc in tunnels, for roads under repair, or for other congested areas. In the following schematic, l is the length of a typical car and d is the distance between cars:

was determined, where d is measured in feet and v in miles per hour. Find the velocity in miles per hour and the corresponding following distance d that maximizes traffic flow. How sensitive is the solution to changes in v? Can you suggest a practical rule? How would you enforce it?

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Justify that the flow rate is given by velocity distance Let's assume a car length of 15 ft. In Section 2.2 the safe stopping distance d = 1.lv +0.054v f=