using uniform acceleration, how can I find the displacement of an object?

If the acceleration is constant and always in the same direction x, and the initial velocity component in that direction is Vox, then the displacement at later times is

X - Xo = Vox t + (a/2)t^2

where Xo is the x-position at time 0.

There may also be a displacement in perpendicular y an z directions, if there was an initial velocity component in those directions