Multiple choice

On a specific highway, the speed-density relationship follows the Greenberg’s model [v = vf In (kj/k)], where v and kj are the free flow speed and jam density respectively. When the highway is operating at capacity, the density obtained as per this model is

  1. e.kj

  2. kj

  3. kj/2

  4. kj/e
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Greenberg's model is v = vf * ln(kj/k). Flow q = v * k = vf * k * ln(kj/k). To find capacity, differentiate q with respect to k and set to 0: dq/dk = vf * (ln(kj/k) - 1) = 0. This implies ln(kj/k) = 1, so kj/k = e, or k = kj/e.

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