Average free flow speed and the jam density observed on a road stretch are 60 km/h and 120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on the road stretch (in vehicles/h) is _________.Correct answer is '1800'. Can you explain this answer?

Question

Answer

Linear speed-density relationship

A linear speed-density relationship is often used to model traffic flow on a road stretch.

It assumes that as the density of vehicles on the road increases, the speed of the vehicles decreases linearly.

This is because as the number of vehicles on the road increases, there is less space between them and this reduces the speed at which they can travel.

Conversely, as the density of vehicles on the road decreases, the speed of the vehicles increases linearly.

Free flow speed and jam density

The free flow speed is the speed at which vehicles can travel on a road stretch when there is no congestion or traffic.

In this case, the free flow speed is 60 km/h.

The jam density is the maximum density of vehicles on a road stretch before traffic comes to a complete stop.

In this case, the jam density is 120 vehicles/km.

Maximum flow

The maximum flow on a road stretch is the highest number of vehicles that can pass through it in an hour.

To calculate the maximum flow, we need to know the maximum density of vehicles that can be on the road at any given time.

This is calculated by taking the difference between the jam density and the density at free flow speed.

In this case, the maximum density of vehicles on the road is 120 - 60 = 60 vehicles/km.

Next, we need to calculate the speed at which the vehicles will be traveling when the density is at its maximum.

This is done using the linear speed-density relationship.

At a density of 60 vehicles/km, the speed of the vehicles will be 30 km/h.

Finally, we can calculate the maximum flow by multiplying the maximum density by the speed of the vehicles.

In this case, the maximum flow is 60 x 30 x 1000 = 1800 vehicles/h.

Therefore, the correct answer is 1800.

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