Consider the flow described by the velocity field \(\vec{V}=\) \(B x(1+A t) \hat{i}+C y \hat{j}\), with \(A=0.5 \mathrm{~s}^{-1}\) and \(B=C=1 \mathrm{~s}^{-1}\). Coordinates are measured in meters. Plot the pathline traced out by the particle that passes through the point \((1,1)\) at time \(t=0\). Compare with the streamlines plotted through the same point at the instants \(t=0,1\), and \(2 \mathrm{~s}\).