A velocity field is given by (vec{V}=a y t hat{i}-b x hat{j}), where (a=1 mathrm{~s}^{-2}) and (b=4

Question:

A velocity field is given by $\vec{V}=a y t \hat{i}-b x \hat{j}$, where $a=1 \mathrm{~s}^{-2}$ and $b=4 \mathrm{~s}^{-1}$. Find the equation of the streamlines at any time $t$. Plot several streamlines at $t=0 \mathrm{~s}, t=1 \mathrm{~s}$, and $t=20 \mathrm{~s}$.