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

Answer 1

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