The position $x$ at time $t$ ($t \geq 0$) of a point P moving on a number line is
$$x = - \frac { 1 } { 3 } t ^ { 3 } + 3 t ^ { 2 } + k \quad ( k \text{ is a constant} )$$
When the acceleration of point P is 0, the position of point P is 40. Find the value of $k$. [4 points]