A question that gives position as a polynomial function of time and asks to find the velocity at the instant when acceleration equals zero, requiring setting the second derivative to zero and evaluating the first derivative.
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]