1. Consider a traffic flow problem where all cars travel at the same speed 1...
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1. Consider a traffic flow problem where all cars travel at the same speed 1 (a) Suppose that the density function at t 0 is (x, 0)-1 if Irl 0 and 2' > 0, Graph (on three aligned axes) as much of the solution (r,t) as you can for0, t1, and t-2 i. Show by drawing a space-time diagram (t vs. r) that if you also know (0,t) (the density of cars leaving the on-ramp), then you do have enough information to find (z, 1) for all z and 1. iii. Suppose that you know that (0,1) 1 for all t > 0, Return to part (i) and complete the sketches of (r, t) (i.e., redraw thenn and include your new information)
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