Question Vehicles moving along a multi-lane road section maintain fixed speeds. Each vehicle, however. moves at its own speed that may differ from the speeds of other vehicles. Vehicle trajectories and speeds in a rectangular area are defined by t = 0 - 1 minute and x = 0 -1 mile (see figure below). a) Estimate the hourly volume, time-mean speed and approximated space-mean speed from the spot observation at point x = 0.1 mi during the period t = 0 - 1 min b) Estimate the traffic density and space mean speed from the instantaneous observation at time t= 0.1 min between point x=0 mi and x=1 mi miles 1.0 47.1 nih 0.9 59.6 22.5 34.2. 0.8 0.71 37.3 46.5 0.6 42.4 0.5 46.5 0.4 30.5 52.6 0.3 0.2. 37.4 47.5 0.1 28.2 0.0 0.0 0.1 0.2 0.3 04 0.5 0.6 0.7 0.8 0.9) 1.0 minute

So first put all your data points into a table as below. We have 13 data points and calculate the average speed Time mean speed = the average of all the speeds and is calculated as follows Time-Mean Speed, bar(v)_(TMS)= avg. speed =(sumv_(i))/(n)=(sum(d)/(t_(i)))/(n) So our time mean speed = 40.946 mph -------------------------------------------------------------------------------------------------------------------- 13 vehicles are observed in 1 minute So flow = 13 veh/min = 780 veh/hour -------------------------------------------------------------------------------------------------------------------------- Space mean speed is calculated by the formula Space-Mean Speed, bar(v)_("SMS ")=(" distance traveled ")/(" avg. travel time ")=(d)/(sumt_(i)_)=(n xx d)/(sumt_(i))where:{:[d,=" distance traveled or length of roadway segment; "],[n,=" number of observations; "],[v_(i),=" speed of the "i" th vehicle; "],[t_(i),=" travel time of the "i" th vehicle; and "],[t_(ri),=" running time of the "i" th vehicle. "]:} So draw a horizontal line at x = 0.1 mile and then calculate it as follows So after drawing horizontal ... See the full answer