I agree with Bob that my method of finding differences is not the best.
Its only advantage is simplicity; I can avoid distructions when the most
obvious method is used. And in the problem at hands this method does give
perfect results when t and d data are perfect, even when time increments
are not very small. But this would not be good for many other problems.
John's approach to data, least square fitting, is OK if the goal is to
find "the best g" from positional data (without calculating individual
v and a). But my goal is to "discover" that acceleration remains constant.
In that situation the step-wise approach is unavoidable. Ideally, the
final result should be a horizontal a=f(t) line for all intervals.