$6-2.$ A study of speed$-$flow$-$density relationships at a particular

site has resulted in the following calibrated relationship:

$S=71\mathrm{.}2(1-\frac{D}{122})$

$($a$)$ Find the free$-$flow speed and jam density for this

relationship.

$($b$)$ Derive equations depicting the relationships

between flow and density, and speed and flow. Plot

the resulting curves. Show the values of free$-$flow,

speed, jam density, and capacity on these curves.

$($c$)$ Determine the capacity of the site mathematically.

$6-3.$ Answer all questions as in problem $6-2$ for the follow$-$

ing speed$-$density relationship:

$S=62e^{-0\mathrm{.}015D}$