Chapter 2, Problem 29P

A flow is described by velocity field $\stackrel{\to }{V}=ay\hat{i}+bt\hat{j}$, where a = 0:2 s⁻¹ and b = 0:4 m/s². At t = 2 s, what are the coordinates of the particle that passed through point (1, 2) at t = 0? At t = 3 s, what are the coordinates of the particle that passed through point (1, 2) at t = 2 s? Plot the pathline and streakline through point (1, 2), and plot the streamlines through the same point at the instants t = 0, 1, 2, and 3 s.