I'm feeling really stupid right now, but anyway; I'm making a game in XNA and it's going pretty well, but the way I was doing movement was causing a strange problem of things 'falling';
(velocity, position and acceleration are all vector2s)

position += velocity * (float)gameTime.ElapsedGameTime.TotalSeconds;
velocity += acceleration * (float)gameTime.ElapsedGameTime.TotalSeconds;

i figured out that this was because i wasn't normalising and fixed it by doing this...

position += entityMovement.entityVelocity * (float)gameTime.ElapsedGameTime.TotalSeconds;
velocity += normalisedAcceleration * (float)gameTime.ElapsedGameTime.TotalSeconds;

Or at least i thought it did, it worked when i did it for bullets the player has fired, but when i put the same code for the player and enemies to use it they just move incredibly slowly, I realised it's because the bullets have a pretty high initial velocity whereas the enemies and player have no initial velocity and that i should probably not be normalising the acceleration...but I can't figure out any other way to do it, can someone please explain to me what it is I should be doing?
I should be normalising just the direction or something?

Thanks for any help.

Why don't you try to just modify velocity with the deltatime. That should give you the correct velocity according to your framerate assuming you got all other conversion units right.

What are you doing, exactly, when you normalize? Are you properly converting the units the objects velocity/acceleration uses to screen units (pixels)? I'll just assume it

I don't know why you would need to normalize anything. You should just be able to add the velocity*TimeSinceLastMovement to the location vector, and you'd be good.
pixels/time * time = pixels (location) changed during the elapsed time

For Acceleration, it should be the same, but adding it to velocity.
pixels/(time^2) * time = pixels/time (velocity) changed during the elapsed time

Just make sure your units are right, and the time you're giving it is the time since you last called. I assume all these values are using floats (or doubles), since you don't want to lose precision by using ints.

What do you mean by pixels in those lines of code? Screen coordinates traveled? or just literally the total number of pixels on the screen (xSize*ySize)?