Two sets of students are collecting traffic data at two sections, xx and yy, of a highway 1500 ft apart. Observations at xx show that five vehicles passed that section at intervals of 3, 4, 3, and 5 sec, respectively. If the speeds of the vehicles were 50, 45, 40, 35, and 30 mi/hr respectively, draw a schematic showing the locations of the vehicles 20 sec after the first vehicle passed section xx. Also determine (a) the time mean speed, (b) the space mean speed, and (c) the density on the highway.
What will be an ideal response?
The distance traversed by each vehicle 20 seconds after crossing section x-x is calculated as follows:
Similarly:
xB = (45)(1.47)(20 – 3) = 1125 ft
xC = (40)(1.47)(20 – 3 – 4) = 764 ft
xD = (35)(1.47)(20 – 3 – 4 – 3) = 515 ft
xE = (30)(1.47)(20 – 3 – 4 – 3 – 5) = 221 ft
a) Time mean speed (TMS), using Equation 6.2, 
ut = (50 + 45 + 40 + 35 + 30) / 5
ut = 40 mi/h
b) Space mean speed (SMS), using Equation 6.3, 
us = 5 / (1/50 + 1/45 + 1/40 + 1/35 + 1/30)
us = 5 / 0.1291
us = 38.7 mi/h
c) Density, 
k = (5 veh / 15 sec)(3600 sec / hr) / (38.7 mi/hr)
k = 31.0 veh/mi
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