Worst part is that they do all this over measly 2030 % off <| sep |> It never reaches zero , but if you add up the total acceleration from t 0 to tinfinity , you still get a finite total . I get what you ' re suggesting now , though incidentally integration is not really addition even if similar and related . E . g . , if you add up accelerations you get an acceleration , but if you integrate acceleration with respect to time you get velocity . Once again , though , this presumes the model is accurate to reality rather than a very good approximation . Our assumptions about reality can lead to an incorrect model e . g . , assuming an absolute reference frame leads to wrong results in certain situations . This is getting far off course from the original discussion , though .