If the flow rate of traffic q as a function of density k is given by
q(k)=vmaxk(kmax−k),
what is the maximum flow rate possible (in cars/hr)?
Assume that vmax is 100 km/hr and kmax is 200 cars/km.
Note: 100 km/hr=60 mi/hr, which is a typical speed limit for a US highway, and midsize cars are approximately 5 m long, corresponding to 200 cars/km in bumper-to-bumper traffic.