This is a continuation of "How to draw Bézier curves recursively": http://scratch.mit.edu/projects/11790017/ The follow up is "How to smoothen edges using a Bézier spline": http://scratch.mit.edu/projects/11839767/ It only works if all points are inside the drawing window. If a particle moves along a parametric curve S(t), you get its velocity V(t) from the derivative of the S(t), you get the acceleration A(t) from the second derivative, V(t)=S'(t) and A(t)=S''(t).
A nice treatment with more math details is given here (pdf): http://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf
