On a specific highway, the speed-density relationship follows the greenberg's model. The free flow velocity is 80 km/hr and jam density is 200 vehicles/km. When the highway is operating at maximum capacity, the density obtained as per this model is _______ veh/km.
73.58

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Solution

The correct option is A 73.58
Greenberg's model is given by,
$υ = υ_{f} I n (\frac{k_{j}}{k})$
$q = k υ$

$\Rightarrow q = k υ_{f} I n (\frac{k_{j}}{k})$

For maximum capacity, $\frac{d q}{d k} = 0$

$\Rightarrow k υ_{f} \times \frac{k}{k_{j}} \times (- \frac{1}{k^{2}}) + υ_{f} I n (\frac{k_{j}}{k}) = 0$

$I n \frac{k_{j}}{k} = 1 = I n (e)$

$\Rightarrow k = \frac{k_{j}}{e} = \frac{200}{e} = 73.58 v e h / k m$

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On a specific highway, the speed-density relationship follows the greenberg's model. The free flow velocity is 80 km/hr and jam density is 200 vehicles/km. When the highway is operating at maximum capacity, the density obtained as per this model is _______ veh/km.73.58

The correct option is A 73.58Greenberg's model is given by, υ=υfIn(kjk) q=kυ ⇒q=kυfIn(kjk) For maximum capacity, dqdk=0 ⇒kυf×kkj×(−1k2)+υfIn(kjk)=0 Inkjk=1=In(e) ⇒k=kje=200e=73.58veh/km

On a specific highway, the speed-density relationship follows the greenberg's model. The free flow velocity is 80 km/hr and jam density is 200 vehicles/km. When the highway is operating at maximum capacity, the density obtained as per this model is _______ veh/km.
73.58