In the velocity or acceleration graph are you integrating acceleration or velocity? In the graph you have velocity in y axis, but there is text telling the graph is about acceleration, so which one is it?

The diagram has velocity on y so the curve describes velocity at each point in time. Acceleration is the slope of the curve. The example starts with (and stores) acceleration and uses it to calc velocities and subsequently integrates velocity over time to get distance.

Is the translation the same as delta velocity?

How did you end up with the formula:

*translation = ( (v0 + v1) x dt ) / 2*

From formula

*v1 = v0 + acceleration × dt*

You get:

*v1 - v0 = acceleration x dt*

But there is no translation there in that formula.

Read this good old article:

http://lolengine.net/blog/2011/12/14/understanding-motion-in-games

When revising the Platformer tutorial I found out the links to ExciteMike explanations on jumps are no longer available, but thanks to a Wayback Machine / Internet Archive I found the resource here:

https://web.archive.org/web/20111118062925/http://meyermike.com/wp/?p=175

https://web.archive.org/web/20111116151429/http://meyermike.com/wp/?p=160

Leaving it here in hope someone could find it interesting perhaps