$(8$ points$)$

A ranger tests his animal tracker.

A turtle walks from their house to the river, and their velocity can be described by the equation

$v(t)=\frac{1}{5}{t}^2,$

where $v(t)$ is in feet per minute.

How far is the turtle from their house after twelve minutes, given that they began at at their house $($when $t=0,$ distance $=0).$