Streaklines are traced out by neutrally buoyant marker fluid injected into a flow field from a fixed point in space. A particle of the marker fluid that is at point \((x, y)\) at time \(t\) must have passed through the injection point \(\left(x_{0}, y_{0}\right)\) at some earlier instant \(t=\tau\). The time history of a marker particle may be found by solving the pathline equations for the initial conditions that \(x=x_{0}, y=y_{0}\) when \(t=\tau\). The present locations of particles on the streakline are obtained by setting \(\tau\) equal to values in the range \(0 \leq \tau \leq t\). Consider the flow field \(\vec{V}=a x(1+b t) \hat{i}+c y \hat{j}\), where \(a=c=1 \mathrm{~s}^{-1}\) and \(b=0.2 \mathrm{~s}^{-1}\). Coordinates are measured in meters. Plot the streakline that passes through the initial point \(\left(x_{0}, y_{0}\right)=(1,1)\), during the interval from \(t=0\) to \(t=3 \mathrm{~s}\). Compare with the streamline plotted through the same point at the instants \(t=0,1\), and \(2 \mathrm{~s}\).