For a traffic stream, v is the space mean speed, k is the density, q is the flow, v_f is the free flow speed, and k_j is the jam density. Assume that the speed decreases linearly with density. Which of the following relation(s) is/are correct?

q = k_j k - (k_j / v_f) k²
q = v_f k - (v_f / k_j) k²
q = v_f v - (v_f / k_j) v²
q = k_j v - (k_j / v_f) v²

Correct answer: q = v_f k - (v_f / k_j) k²

Solution

The correct option describes the relationship between flow, density, and speed in a traffic stream where flow decreases quadratically with density. This aligns with the assumption of linear speed decrease with density, ensuring that as density increases, flow is accurately modeled.

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