Problem$3(25$ pts$.)$: An engineer is conducting a traffic study on a single$-$lane urban road to determine the vehicular flow rate. Observations indicate that vehicles maintain a steady speed of $100k\frac{m}{h}$ and a uniform headway of $100$ meters.

A$.$ Calculate the flow rate $($in vehicles per hour$)$ expected at a fixed point on this road over a $15$ minute interval.

$10pts$

B$.$ Considering the observation is conducted at a broader scale and is subject to the SpeedDensity linear Relationship, as depicted in the accompanying figure, determine the flow capacity of the road.

$10pts$

C$.$ How might the Speed$-$Density linear Relationship be affected under variable traffic volumes, diverse vehicle types, and different weather conditions?

$5pts$

$($Show all your work! Provide units with your answer and circle you answer.$)$