The data shown below were obtained by time-lapse photography on a highway. Use regression analysis to fit these data to the Greenshields model and determine the following. Speed (mi/h) Density (veh/mi) 84 16.2 24.7 69 33.3 54 39.7 40 52.0 19 55.1 14 (a) the mean free speed (in mi/h) mi/h (b) the jam density (in veh/mi) veh/mi (c) the capacity (in veh/h) veh/h (d) the speed at maximum flow (in mi/h) mi/h

Given a freeway flow study at a certain highway. The speed- density relationship is described in the givenequation or relationship: V s = 58- 0.40k Determine the following:a. Free-flow speed and jam densityb. Derive the equation describing flow and speed.c. Derive the equation describing flow and density.d. Determine the capacity of highway

4. The statistical data of an urban spot speed study is given below. A set of 130 observations of spot speeds made by timing vehicles through a "Trap" of 88ft. The stopwatch was used to obtain data. The stopwatch data are grouped into 0.2 sec. Classes. The first column of the table shows the midpoint of each group. The second column of the table shows the frequency of the observations. Compute the following statistical values. a) The speed of each time class in mph (show it in the third column) b) The cumulative percent of vehicles traveling at or below indicated speed shown in the third column in mph (show it in the forth column) c) Mean or average speed (time-mean speed), median, mode, standard deviation, standard error of the mean, average time, space-mean speed, variance, 15%, and 85% speed. d) Plot the cumulative percentage, and show the statistical values of item (c) on the graph. e) Plot the frequency distribution curve and show the statistical values on the graph.