<< Graphics`ImplicitPlot`

    InitCond[x_] = Exp[-x]

    FluxFunc[u_] = u^2/2

    WaveSpeed[x_] =  FluxFunc'[InitCond[x]]
  
  

    Show[Table[
        ParametricPlot[{x, (x - xnaught)/
              WaveSpeed[xnaught]}, {x, -15, 15}, 
          PlotRange -> {0, 5}], {xnaught, -15, 
          15,  .5}]]