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GATE 2025 CE (CE1) – Question 40

Traffic Engineering and Transportation Planning · Fundamental relationships of traffic flow · 2 marks · Multiple choice

The speed-density relation on a one-way, single lane road is shown in the figure, where speed $u$ is in km/hour and density $k$ is in vehicles/km. The maximum flow (in vehicles/hour) on this road is

A graph of speed $u$ against density $k$. The speed is constant at 90 km/h from $k = 0$ to $k = 10$, and then falls along a straight line to zero at $k = 100$.
  1. 2500
  2. 900
  3. 2250
  4. 2000

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Correct answer: (A) 2500

Explanation

The flow is $q = ku$. For $k \le 10$, $u = 90$ and $q = 90k$, which reaches 900 at $k = 10$. For $10 \le k \le 100$ the line gives $u = 100 - k$, so $q = k(100 - k)$, which has its maximum where $100 - 2k = 0$, at $k = 50$, giving $q = 50 \times 50 = 2500$ veh/h. That is larger than the 900 at the end of the first part.