A transient flow field is given by $V=Ay{e}^{-ct}$hat$(i)+$Bhat$(j)$ where $x$ and $y$ are in meters, $A=\frac{3}{s},B=2\frac{m}{s},$ and $c=\frac{0\mathrm{.}5}{s}.$

Determine and plot the streamlines for the flow that passes through the origin at $t=0,3s,$ and $6$ s $.$ Determine the value of $y$ at $x=3$ m for each of these times.

At $t=0$

$y=$ m

At $t=3s,y=$ m

At $t=6s,y=$ bs

$2.$ Determine the pathline for the particle that passes through the origin at $t=0.$ The $y-$values for the pathline are

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