Homework 8
Due Friday,
March 28, 2008
Question 1
s = 0.3/(60-u)
k = 1/s = (60-u)/0.3
u = 0.3 k – 60
q = uk
Therefore,
q = 0.3 k2 -60 k
for max q, dq/dk = 0
Therefore, k = 100
Max q = 3000 veh/hr
Question 2
u = -0.47 k + 60 (best fit line)
multiply by k to give q-k equation
q = - 0.47 k2 + 60 k
u max, du/dk = 0
gives at qmax, k = 63.8 vehicles/mile
qmax = 1914 vehicles/hr
k(jam) = 128 vehicles/mile
Question 3
Speed of shockwave at front of platoon is 0 mph (traffic is stopped)
Speed of shockwave at black of platoon is -8.57 mph (0 – 1200) / (240 – 100)
Speed of shockwave at front on release is -10 mph (1600 – 0) / (80 - 240)
We did not cover the graphing asked for in the question.
Question 4
Speed of shockwave at black of platoon is -2.86 mph
Speed of shockwave at front on release is -15 mph
Rate at which the platoon is decreasing is (-2.86) – (15) = 12.15 mph
Time for platoon to dissipate 3 mi/12.15 mph = 0.25 hr = 15 min
Speed of new shockwave after platoon disappears is 13.3 mph
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