Return the sphere to the origin. Group it and move the group node in X five units. Lots of time you ll group nodes so that you have more control over their motion. In the above example you might have a group node for translation, a group node for rotation, and a group node for scale. The docs describe world space as your camera view with the origin at the center.
Local space is described as the space around an entity with the origin at the center of that entity.
Well if you are going to calculate acceleration in local space it's pretty easy. All you have to do is use the getAttr function in an expression using the frame option. The main problem with this is that xform does not have a time function like getAttr does, so you have to use a variable that acts as a place holder for the value from the frame before. Another problem with this setup is that it forces you to run through the entire animation to get the correct value because it compares the place holder value with the current value. It sorta starts acting like a dynamic simulation, which just means that when you try scrubbing the frame slider you get incorrect results.