Problem 2. Consider a traffic flow problem where all cars travel at the same spe

Question

Problem 2. Consider a traffic flow problem where all cars travel at the same speed 1 (a) Suppose that the density function at t 0 is ?(z,0)-1 ?? 0 and >0 Draw (on the same z-axes) as much of the solution pz,t) as you can for t-0,t-1,t 2 ) Show by drawing a space-time diagram, that if you also know p(0,t) (ie. the density of cars leaving the on ramp), then you do have enough information to find p(r, t) for all z and t (i) Suppose that you know that ?(0,t)-1 for all t 2 0, return to part (i) and complete the sketches of ?(z,t).

Explanation / Answer

i) as the density function of the given equation p(x) is not given so the resultant parameters are not there in the function so the p(x, t) can't be find in this case.

ii) if p(0,t) is known then it is easy to find the space & parameters for the given equation so the time interval could be find in that case.

iii) if p(x, t) =1 then the required equation could have a straight line on the graph.

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