Problem $2(15\%)$Problem $3(15\%)$

The following relationship applies to a particular urban highway:

$u=20ln(\frac{240}{k})$

where $u$ and $k$ are the traffic stream speed and density, respectively.

Calculate $q_c($or capacity$),u_m$ and $k_m($optimum speed and density corresponding to

capacity$).$

Calculate the density when $q=1000vph.$

The following spot speeds have been measured through a radar gun on an overpass bridge:

find the time$-$mean speed and space$-$mean speed.

list the cumulative observations and relative cumulative observations $($on a $100$ percent

scale$),$ and find

a$)$ the median speed

b$)85$ percentile speed

c$)15$ percentile speed

d$)$ the pace