Problem Statement: Observations on a section of highway indicate that traffic follows the Greenshields linear speed-density model. Field measurements show the free-flow speed ($u_f$) is 80 kph and the jam density ($k_j$) is 100 vehicles per kilometer.

Calculate the theoretical maximum flow (capacity) of this highway segment, and determine the optimal speed and density at which this capacity occurs.

Problem Statement: Traffic observations on a highway segment show that the average vehicle density is 45 vehicles per mile (veh/mi) and the space-mean speed of the traffic stream is 40 miles per hour (mph). Calculate the traffic flow rate ($q$) in vehicles per hour (veh/h).

Given: The fundamental equation of traffic flow is:

Problem Statement: A traffic stream is operating at a capacity flow ($q_1$) of 2,000 veh/h with a density ($k_1$) of 50 veh/mi. An accident occurs, completely blocking the road. In the fully stopped queue (state 2), the flow ($q_2$) is 0 veh/h, and the jam density ($k_2$) is 250 veh/mi. Calculate the velocity of the resulting backward-moving shockwave.

Given: The velocity of a shockwave ($u_{sw}$) is defined as the change in flow divided by the change in density:

Problem Statement: During a 15-minute observation period, 300 vehicles pass a specific point on a highway. Calculate the flow rate in vehicles per hour, and determine the average time headway between vehicles in seconds.