Question

Consider the four points P, Q, R, and S shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by \( k_P \), \( k_Q \), \( k_R \), and \( k_S \), respectively. The correct order of these densities is: 
 

• A. \( k_P > k_Q > k_R > k_S \)
• B. \( k_S > k_R > k_Q > k_P \)
• C. \( k_Q > k_R > k_S > k_P \)
• D. \( k_Q > k_R > k_P > k_S \)

Hint:

In speed-flow diagrams, density decreases as flow increases past the optimal capacity point, corresponding to increasing congestion.

Answer 1

The Correct Option is A

In the Greenshields fundamental speed-flow diagram, the traffic density is typically highest at the lowest flow and lowest at the highest flow. The diagram shows the relationship between speed, flow, and density, and based on the shape of the curve:
- Point P represents the condition with low flow and high speed, which corresponds to high traffic density \( k_P \).
- Point Q is closer to the optimal flow condition, where the speed begins to decrease as the flow increases, leading to the second highest density \( k_Q \).
- Point R represents a higher flow and lower speed, which leads to a lower traffic density \( k_R \).
- Point S represents the maximum flow point, beyond which traffic congestion occurs, and the density \( k_S \) is the lowest.
Thus, the order of the traffic densities is \( k_P > k_Q > k_R > k_S \). Final Answer: (A) \( k_P > k_Q > k_R > k_S \)