Problem $1\mathrm{.}14$:

A retired traffic engineer cycles every day at different times along the same route. His $0\mathrm{.}8km$ bike route is parallel with the roadway as shown in Figure $1\mathrm{.}19$ below. Being a traffic engineer, he made a habit of counting the number of cars in lane $A$ on the roadway overtaking him $(M_o)$ and he overtook $(M_p)$ while riding Northward and the number of cars that he met while riding Southward $(M_S).$ Table $1\mathrm{.}6$ below summarizes the average count he obtained for each different period of the day. Given that he cycles at the constant speed of $32k\frac{m}{h}$ and assuming a linear speed$-$density relationship:

$($a$)$ Find the traffic stream conditions $($flow$,$ speed and density$)$ for each period of the day $($show complete calculation for one of the periods, and summarized$/$tabulate the rest$)$;

$($b$)$ Plot and establish the speed$-$density relationship for the traffic stream;

$($c$)$ Estimate the capacity of lane A;

$($d$)$ Determine the spacings when flow is $1200ve\frac{h}{h}$; and

$($e$)$ Sketch the flow$-$density relationship, show all corresponding values and state the traffic conditions on the sketch.

Table $1\mathrm{.}6$ Average count for each period of time.

$\backslash$table$[[$Time of day,$M_S,M_0,M_p$