(1) Describe in your own words the differences between streamlines, streaklines, and pathlines.

A velocity field is given by \[\mathbf{V} = A x \hat{i} - A y \hat{j}\] the units of velocity are m/s, \(x\) and \(y\) are given in meters, and \(A = 0.3\) \(s^{-1}\).

(2) Obtain an equation for the streamlines in the \(xy\) plane.

(3) Plot the streamline passing through the point \((x_0, y_0) = (2,8)\) using appropriate software

(4) Determine the velocity of a particle at the point (2,8)

(5) If the particle passing through the point \((x_0, y_0)\) is marked at time \(t = 0\), determine the location of the particle at time \(t = 6\) s.

(6) What is the velocity of this particle at time \(t = 6\) s?

(7) Show that the equation of the particle path (the pathline) for this flow is the same as the equation of the streamline.