Simple Physics In Computer Games. (2D)

I use simple physics in my games to simulate gravity on objects. My characters who run, slide
and jump around all use simple physics to create a realistic effect.
I learned how to implement these things by reading around various articles.
I will try to find the article that helped me most out of the lot and provide a link to it.

Objects jumping around.
If your main character is meant to jump around on platforms then you probably want them to
look fairly realistic doing it. My objects have a position in the world (x and y) and if
they can move then they also have velocity x and y values too. These are the ones that make
it all happen.

Each time the object is updated, the velocity of the object is applied to the objects position.
If you change the value of its velocity then you change the speed and the direction it moves.

Depending on the view of your game, gravity and other forces that need to be applied to your 
object need to be implemented accordingly.
If you have a side view and your object is moving upwards (negative y velocity) then you need
to increase the y velocity over each frame until it eventually stops in mid air (briefly) and
starts to fall (a positive y velocity).

Falling and hitting the ground.
When the y velocity value is positive the object is moving down the screen, we want this to
reach a maximum velocity until it hits some solid ground. So we have to either find out how
far it is to solid ground or we check if we have something to stand on each frame.