Calculating position given initial position, velocity and acceleration

[SLH]

I'm creating a 2D game that supports replays by creatubg keyframes every time the object's properties change not according to a formula.

Currently i'm moving the object using the following formulas (where Timing.dt) is the amount of time passed:

float XChange = Velocity.X * Timing.dt + Acceleration.X * (Timing.dt * Timing.dt) / 2.0f;
float YChange = Velocity.Y * Timing.dt + Acceleration.Y * (Timing.dt * Timing.dt) / 2.0f;
Position.X += XChange;
Velocity.X += Acceleration.X * Timing.dt;
Position.Y += YChange;
Velocity.Y += Acceleration.Y * Timing.dt;

However, what i'd like to be able to do is, when replaying, jump straight to time t, rather than have to continually apply this algorithm in a loop until i get from my keyframe, to the required time. Unless i'm mistaken, if i change Timing.dt the object's position won't end up the same for a given time (i.e. i can't double Timing.dt and do half as many steps).

So i want a formula for the object's position at time t, given it's initial position, initial velocity and acceleration (constant).

Any help is, of course, greatly appreciated.