Practice Question: Space Mean Speed Along a Freeway

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Solution

Answer: B) 48 mph

Refer to PE Civil Reference Handbook Section 5.1.1.2 for space mean speed definition and equation.

\[U_{s} =  \frac{Flow}{Density} = \frac{q}{k}\]
where: 

\(U_{s} = \text{Space mean speed (mph)}\)

\(\text{q= equivalent hourly flow (vph)}\\\)

\(\text{k = traffic density (vehicle per unit distance)}\\\)

per 5.1.1.1 equivalent hourly rate traffic flow
\[q =  \frac{n(3600)}{T}\\\]
where:

\(n = \text{number of vehicles passing some designated road point}\)

\(T = \text{time in seconds}\)

\[q= (200/60) \times 3600 = 12000\ vehicle\ per\ hr\]

(input data is vehicle per minute and should be divided by 60 to get it to units of vehicle per second)

\[k =  \frac{n}{l}  \\\]
where:

 \(n = \text{number of vehicles per segment of road}\)

\(l = \text{segment length of the road}\)

 

\[k= \frac{5000}{20}=250\ \frac{vehicle}{mile}\\\]
\[U_{s}  = \frac{q}{k} = \frac{12000}{250}=48\ mph\\\]
 

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