Problem $3$

By assuming a linear speed$-$density relationship, the mean free flow speed on a highway facility lane equals $65mph.$ The jam density is observed to be about $170vpm.$

Plot the q$-$k$-$u curves

Write down the speed$-$density and flow$-$density equations

Find the maximum flow

Compute the speeds and densities corresponding to a flow rate of $1,000vph,$ describing the associated traffic conditions.

Calculate the average headways and spacing at maximum flow and at jam density.