Okay everyone. The answer to this might be easy or not...

Given an object with the following variables:

Velocity X

Max Speed

Rate of acceleration and deceleration

Distance to target

How do I know when to decelerate to arrive at the target and have 0 velocity when I do. Basically I have an object that needs to accelerate towards a target and then begin decelerating at the right time.

I Was looking around and found some physics equations that give me things like distance = Acceleration * time ^2 but that doesn't help much... position = position + velocity is how velocity integration works in most games and that gives a different number than physics equations (euler explicit integration???) I don't know what I am talking about but all I know is I spent 3 hour trying to figure out how to calculate when to slow down with no luck and google didn't help