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Problem 1 [20 pts] Assuming that the space mean speed of a single-lane freeway decreases linearly with the density. The speed-density relationship is shown below: k u = 65(1- 160 where u space-mean speed in mph, k = density in vpm (1) Find the free-flow speed (uf), the critical density (kc), and the jam density (k;). (2) Mathematically derive equations depicting the relationships between flow (q) and density (k). Write the quadratic equation that you derived in vertex form: q = a(kb)² + c, where (b, c) = vertex and a is the leading coefficient. Please find a, b, c. (3) Given k>ke and q = 2200vph, what is the value of u (mph) (4) Given k ≤k and q = 2200vph, what is the value of u (mph) (5) What is the capacity (vpm) of this single-lane freeway?

Problem 1 [20 pts] Assuming that the space mean speed of a single-lane freeway decreases linearly with the density. The speed-density relationship is shown below: k u = 65(1- 160 where u space-mean speed in mph, k = density in vpm (1) Find the free-flow speed (uf), the critical density (kc), and the jam density (k;). (2) Mathematically derive equations depicting the relationships between flow (q) and density (k). Write the quadratic equation that you derived in vertex form: q = a(kb)² + c, where (b, c) = vertex and a is the leading coefficient. Please find a, b, c. (3) Given k>ke and q = 2200vph, what is the value of u (mph) (4) Given k ≤k and q = 2200vph, what is the value of u (mph) (5) What is the capacity (vpm) of this single-lane freeway?

Traffic and Highway Engineering
Traffic and Highway Engineering
5th Edition
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Garber, Nicholas J.
Chapter6: Fundamental Principles Of Traffic Flow
Section: Chapter Questions
Problem 13P
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Problem 1 [20 pts] Assuming that the space mean speed of a single-lane freeway decreases linearly with the density. The speed-density relationship is shown below: k u = 65(1- 160 where u space-mean speed in mph, k = density in vpm (1) Find the free-flow speed (uf), the critical density (kc), and the jam density (k;). (2) Mathematically derive equations depicting the relationships between flow (q) and density (k). Write the quadratic equation that you derived in vertex form: q = a(kb)² + c, where (b, c) = vertex and a is the leading coefficient. Please find a, b, c. (3) Given k>ke and q = 2200vph, what is the value of u (mph) (4) Given k ≤k and q = 2200vph, what is the value of u (mph) (5) What is the capacity (vpm) of this single-lane freeway?
Transcribed Image Text:Problem 1 [20 pts] Assuming that the space mean speed of a single-lane freeway decreases linearly with the density. The speed-density relationship is shown below: k u = 65(1- 160 where u space-mean speed in mph, k = density in vpm (1) Find the free-flow speed (uf), the critical density (kc), and the jam density (k;). (2) Mathematically derive equations depicting the relationships between flow (q) and density (k). Write the quadratic equation that you derived in vertex form: q = a(kb)² + c, where (b, c) = vertex and a is the leading coefficient. Please find a, b, c. (3) Given k>ke and q = 2200vph, what is the value of u (mph) (4) Given k ≤k and q = 2200vph, what is the value of u (mph) (5) What is the capacity (vpm) of this single-lane freeway?
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