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B Consider a single-lane highway with the free-flow speed of 80km/hourand the jam density of 100 vehicles /km. In normal traffic condition, vehicles are travelling

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Consider a single-lane highway with the free-flow speed of 80km/hourand the jam density of 100 vehicles /km. In normal traffic condition, vehicles are travelling at the speed of 64km/hour. On one day, a heavy truck with the speed of 8km/hour entered the highway, traveled 0.5kmat the same speed and exited the highway. Consequently, the vehicles immediately behind the truck had to lower the speed to 8km/hour behind the truck and formed a platoon with the density of 90 vehicles/km and the flow of 720 vehicles/hour. Apply the Greenshields' model or the shock wave theory to determine: (a) The capacity and the density at capacity of the vehicle flow; (b) The length of the platoon immediately after the truck exited; (c) The time it took for the platoon to dissipate after the truck exited. Assume that there was no congestion on the road further downstream of the point where the truck exited.

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