As per green shields model,

The relationship between traffic speed and density is described using a negatively sloped straight line, known as the traffic flow diagram. This diagram plots the speed of vehicles against the density of vehicles on a roadway. At low densities, the speed is high, indicating free-flow conditions. As the density increases, the speed decreases, indicating congestion.

The free-flow speed (vf) represents the maximum speed at which vehicles can travel on a roadway when there is no congestion. It is the speed at which traffic flows smoothly and efficiently with minimal interruptions. In this scenario, the density of vehicles is low, and the speed is at its highest.

The maximum flow occurs at a speed lower than the free-flow speed. This is because as the density of vehicles increases, the capacity of the roadway decreases. At a certain point, the flow of vehicles reaches its maximum, and any further increase in density leads to congestion and a decrease in flow.

To find the speed at which the maximum flow occurs, we divide the free-flow speed (vf) by 2. This is represented by option C in the given choices. Dividing the free-flow speed by 2 indicates that the maximum flow occurs at a speed that is half of the free-flow speed.

This relationship can be explained by the fundamental diagram of traffic flow, which consists of three regions: free-flow, congestion, and breakdown. In the free-flow region, traffic moves smoothly, and the speed is high. As the density increases, the flow transitions into the congestion region, where the speed decreases due to increased interactions between vehicles. Finally, at very high densities, the flow reaches the breakdown region, where the speed is extremely low, and the traffic comes to a standstill.

By dividing the free-flow speed by 2, we identify the speed at which the maximum flow occurs, which is in the congestion region of the traffic flow diagram. This speed represents an optimal balance between vehicle density and speed, maximizing the flow of vehicles on the roadway.