The density$-$speed relationship for a freeway lane was found to be:

$u=54\mathrm{.}5-0\mathrm{.}24k$

Speed is given by $u,$ density is given by $k,$ and flow is given by $q.$ Determine:

a$.$ speed at capacity

b$.$ density at capacity

c$.$ free flow speed

d$.$ maximum flow

e$.$ Sketch the $u-q,q-k$ and $u-k$ curves for this stream flow equation.