Assuming you are talking about a constant acceleration, what you are looking for is
[tex]
d=\frac{1}{2}at^2+v_0 t
[/tex]
where [itex]d[/itex] is the total distance traveled, [itex]a[/itex] is the acceleration, [itex]v_0[/itex] is the initial velocity but you said you will be taking that as zero. If you know calculus, the way you arrive at this formula comes simply from integrating the constant acceleration twice; in other words, with calculus you can say that the integral of acceleration (where the integration variable is time) is velocity, and the integral of velocity (integration variable also time) is position.