Originally posted by superb00b
...but with a few more sampling points as suggested by djvapor you can construct a piecewise linear curve to integrate, or if you really wanted, use some higher order interpolation to construct a curve...
This is an entirely sound approach, especially since you will be integrating rather than differentiating. The only thing I would change would be to say that, instead of interpolation, you would be using least squares to construct an equation for velocity versus time. That equation will no doubt have errors, but the integration process will cause many of those errors to cancel each other out. Of course, there is no way to know how accurate your model is without actually measuring the distance, but I'll bet least squares would give you a good estimate. (If I am all wet, please be gentle. It has been 23 years since I was in engineering school.)