Traffic on a section of an arterial road is flowing at a space mean speed of 45km/hr. The relationship between space mean speed and density of the traffic on the road section can be described using the following equation (where v represents space mean speed in km/hr and k represents the density in veh/km): v = 80(1-) 160 An octogenarian, travelling to an auto-show, turns onto the roadway at 9am, 4km from the beginning of the arterial road, driving at 25km/hr in a vintage Model T Ford. The vehicle impedes traffic; however, vehicles can pass the slow-moving vehicle resulting in an average space mean speed of 35km/hr upstream of the slow vehicle. The Model T Ford turns off onto a local road from the arterial road 5km after joining the traffic stream and at this point in time vehicles begin to move at the maximum flow rate. Use a space time-diagram and shockwave theory to describe this traffic event. Not all trajectories need to be presented; representative trajectories should be used to describe the flow across all the different traffic regions. Determine: the speed of each shock wave, the points of intersection of each of the shockwaves and the time taken for the congestion to dissipate (when the impact of the slow moving vehicle no longer exists).