CME 302 SAMPLE Midterm_solution

# CME 302 SAMPLE Midterm_solution - CME 302 Midterm Fall 2005...

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Name___________________ This is an open-book, open-note exam. Try to be as specific and detailed as possible in your answers because every step counts! 1. Consider the following between speed, density and flow: u = 70 – k , 0 k 30 (1) Solve analytically for the remaining relationships relating flow, density and speed; (2) plot the fundamental diagrams of traffic flow based on the relationships. Be sure to label all axes and relationships, including the end points of each function; (3) what are the maximum flow, speed at maximum flow, and density at maximum flow? (20 pts) (1) q = uk, and u = 70-k, 0 k 30 (given) q = u(70-u) = 70u – u 2 , 40 u 70 q = (70-k)k = 70k – k 2 , 0 k 30 (2) Speed versus density 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 density speed Speed versus flow 0 10 20 30 40 50 60 70 80 0 200 400 600 800 1000 1200 1400 flow Flow versus density 0 200 400 600 800 1000 1200 1400 0 5 10 15 20 25 30 1

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CME 302 SAMPLE Midterm_solution - CME 302 Midterm Fall 2005...

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