Let the velocity field be given by V = Vm(1 - p^2 / pm), where Vm and Pm are the maximum velocity and maximum traffic density respectively, and let the initial traffic density be 0 < s < Pm(L - E) / (5,0) = T > 3 > 0 < V^2L / 0. EL
(a) Sketch the initial density;
(b) Determine and sketch the characteristics in the x-t plane;
(c) Determine p(x,t) for t > 0.