Problem $5(20\%)$

In a segment of a highway, a total flow of $1500ve\frac{h}{h}$ is observed. All the vehicles are homogeneous and travel at $44\mathrm{.}4k\frac{m}{h}.$ You know that traffic can be modelled by:

$v=0\mathrm{.}5v_f*(1+[1-\frac{q}{1950}{]}^{\frac{1}{2}})$

For $q1950,$ where $v$ represents speed, $v_f$ free$-$flow speed, and $q$ flow. Determine the value of $v_f,$ the jam density, and the maximum capacity of the highway.