which is identical to the result, equation 67.3, obtained by transforming the partial differential equation to a coordinate system moving with the velocity c. EXERCISES 69.1. Show that for an observer moving with the traffic, the rate of change of the measured density is where u is the car's velocity. de - (u - do) de = 69.2. Suppose for graphical purposes that we replace by y, and hence equation 69.1 becomes ap + c = 0. dy дх (a) For what two-dimensional vectors & does g.Vp₁ = 0? (b) Briefly explain why g is perpendicular to Vp1. (c) Using part (b), explain why the curves along which p, is constant must be parallel to g. (d) Show that the results of part (c) are in agreement with the results of Secs. 67-69. A SAMSUNG 940)