Actually, it is pretty trivial.

I know this is a very old thread, but for anyone who reads it, here you go.

Velocity is the change in position with respect to time.

In order to extract velocity from this, you subtract the position on frame 1, from the position on frame 2, and divide by the time elapsed--usually 1/24 or 1/30 depending on your frames per second. Store that value in an array, because you're going to need it later. Go through all of the frames between the curves doing that--position on current frame, minus position on the previous frame, and divide by 1/24.

Next, you want acceleration. Acceleration is the change in velocity with respect to time. Same thing as before. Take the velocity on frame 2, subtract the velocity on frame 1, divide this difference by the elapsed time, 1/24. Store it in an array. Do this all of the way through.

Done.

Edit: Did not see that Vroon already answered this. Maybe my answer gives a little better detail...