GATE 2019 CE (CE2) – Question 56

Traffic Engineering and Transportation Planning · Fundamental relationships of traffic flow · 2 marks · Numerical answer

A highway speed–density relationship is u = 100 − 0.5k, where u is km/h and k vehicles/km. Find maximum hourly flow, to the nearest integer.

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Correct answer: 5000 to 5000

Explanation

Flow is $q=uk=100k-0.5k^2$. Set derivative $100-k=0$ to obtain k = 100 vehicles/km. Speed there is 50 km/h, so capacity is **5000 vehicles/h**.