As part of my waypoint following algorythem, I want my character to accellerate towards a waypoint untill it reaches a point (that should be half way) where it must start accellerateing in the opposite direction to stop in-time, landing on the waypoint.
My character has three Vector2D(double x, double y) vectors; position, velocity and acceleration.
currently my waypoint following logic is;
// if there are waypoints left to go to
if(waypoints.Size() > 0)
{
boolean x = NavigateToWaypoint(waypoints.Peek());
if(x)
{
waypoints.Pop();
}
else
{
STOP();
}
}
the STOP() method just sets the ‘i am navigateing now’ flag to false, stopping the Update() method for my navigation class from running.
NavigateToWaypoint(Vector2D waypoint)
{
if( // stopping distance > distance to waypoint)
{
// break by accellerateing in opposite direction to waypoint.
return false;
}
else if( // stopping distance < distance to waypoint )
{
// accellerate towards waypoint ('ahead full impulse!')
return false;
}
else if(distance to waypoint < 100)
{
// stop the ship, we're there
return true;
}
}
what i’m asking here is how to calculate the stopping distance X for velocity V at acceleration A.
I know its somthing similar to v(end) = v(start) * 2/AX but i’m also sure that this is not it 
I used to know all these formuli back at school - now I cant for the life of me remember what it is, and serching around on google has got me lots of equations that are either way too complicated (wikipedia 
) or not anything I recognise.
if theres any math guys out there who can gove me some hints that would be great.