GATE CE 2021 Set 2 — Question 23
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Transportation Engineering → Traffic Studies & Flow → Speed-Density-Flow
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Question
Relationship between traffic speed and density is described using a negatively sloped straight line. If is the free-flow speed then the speed at which the maximum flow occurs is
Correct answer
(C) (v_f)/(2)
Solution
The relationship between traffic speed () and density () is given as a negatively sloped straight line, which corresponds to the Greenshields model:where is the free-flow speed and is the jam density.
Traffic flow () is defined as:To find the maximum flow, we differentiate with respect to and set it to zero:Substituting back into the speed-density equation to find the speed at maximum flow ():Thus, the speed at which maximum flow occurs is .
Traffic flow () is defined as:To find the maximum flow, we differentiate with respect to and set it to zero:Substituting back into the speed-density equation to find the speed at maximum flow ():Thus, the speed at which maximum flow occurs is .
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