Tiny hydrogen bubbles are being used as tracers to visualize a flow. All the bubbles are generated at the origin \((x=0, y=0)\). The velocity field is unsteady and obeys the equations:

\[\begin{array}{lll} u=1 \mathrm{~m} / \mathrm{s} & v=2 \mathrm{~m} / \mathrm{s} & 0 \leq t<2 \mathrm{~s} \\ u=0 & v=-1 \mathrm{~m} / \mathrm{s} & 0 \leq t \leq 4 \mathrm{~s} \end{array}\]

Plot the pathlines of bubbles that leave the origin at \(t=0,1,2,3\), and \(4 \mathrm{~s}\). Mark the locations of these five bubbles at \(t=4 \mathrm{~s}\). Use a dashed line to indicate the position of a streakline at \(t=4 \mathrm{~s}\).