GRAVITY:

One of the most basic Physics concepts that you might want to implement in a game is gravity.  Whether it be in a platformer, a pinball game, or something else, gravity is a common need.  So to start off, we need to ask ourselves, what it gravity?  Gravity acts on all objects on earth, and pulls the objects towards the surface, we all know that.  But its not merely as simple as decreasing the players position by 1 each frame, things don't fall that way*, as they fall they get faster and faster.  This phenomenom is known as acceleration and is the concept behind gravity and all accelerating physics.

Acceleration is measured in X Meters per second per second.  That is to say, every second, your velocity will increase by X Meters per second.  Since we live in the game world, it would be more somthing like X pixels per frame per frame.  That is to say, every frame, your velocity will increase by X pixels per frame.  Lets say your position starts at 0 and your velocity starts at -3 and you are in an empty world with 1 P/F/F
acceleration (1 pixels per frame per frame).  This chart shows your position, velocity, and acceleration for a few frames

Frame Position Velocity Acceleration
0 0 -3 1
1 -3 -2 1
2 -5 -1 1
3 -6 0 1
4 -6 1 1
5 -5 2 1
6 -3 3 1
7 0 4 1
8 4 5 1
9 9 6 1
10 15 7 1
The code for this would look something like

0->X
-3->V
1->A

While 1
Output(1,1,X)
X+V->X
V+A->V
End
Notice that even when the velocity is positive, the position can still be negative, and vica versa.  But you can see that the position starts off moving downwards, stops at -6, then starts moving upwards again.  Acceleration stays constant througout the entire simulation.  If you want to get really technical, you can go into how velocity is the derivative of position blah blah blah, but you dont need to know that in a game

HOW TO USE IT:

Implementing acceleration is simple, especialy if your acceleration is constant.  You only need a single variable for your position and one for your velocity.  If you want changing acceleration you could add a variable for that too.

Also note that X velocity is INDEPENDANT of Y velocity.  That is to say, if your character has a velocity in the X direction, and has gravity affecting it, since gravity is only in the Y direction (unless your game is uber cool) the Y acceleration will only affect the Y velocity will only affect the Y position.  Try this example program for size:

ZStandard
ZInteger
AxesOff
Clrdraw
0->X
0->Z
0->A
0->B

While 1
PtOff(X,Z,2
X+A->X
Z+B->Z
PtOn(X,Z,2
getKey->K
A+(K=26)-(K=24)->A
B+(K=25)-(K=34)->B
End
Its a fun example of the power of acceleration, see if you can add gravity to it!  You might have some interesting results.

WHAT TO WATCH OUT FOR:

Acceleration is not always applied, for example when you are standing on a platform, both your velocity and your acceleration are 0.  More on this will be covered in the next section 'Collisions'

Good tutorial! I can't wait for what you have to say on collisions with acceleration; I've always wondered how to prevent accelerating through something.

All this does is remind me of how I never paid enough attention in Physics class. xP
Nice to see my wasted education in code form though. I sometimes have a hard time taking real life concepts and converting them to code effectively.

Thanks, that is pretty sweet. I'm gonna have to go over it more though since I still don't quite understand. What would you even use though for your gravity acceleration? I mean gravity in real life is 9.81... m/s² (and 32... ft/s² but I don't think that would work very well on the graph/home screen. But I don't know.

Hmmm, ok. That makes sense. Thanks.

As a general rule you don't want your player moving too fast because that makes collision very difficult.

True, else stuff like this happens

That's really awesome Builderboy!  Thanks, and I can't wait for collisions!   
 *ZTrumpet thinks about making some sort of physics game with Axe with this new knowledge...

btw, since there are people who are visual, it might be a good idea to have some eye candy of the examples in action. Just a suggestion for the tutorial