Problem $2$:

A velocity field has been measured and its vector can be expressed as vec$(v)=3$tvec$()+$xyvec$()+t{y}^2$vec$(k),$ where $x,y,z$ are coordinates in a Eulerian reference and $t$ is time. $(1)$ Determine the acceleration as a function of $x,y,z,t.(2)$ What is the acceleration at a location $x=3m,y=1\mathrm{.}5m,z=0m,$ and time $t=5s?$