Suppose you want to go at a linear rate from point A to point B in four frames. Where would you be at frame 1? At frame 2? At 3? At 4? You probably imagine points along a line similar to one pictured above.
Here's the thing, though: frames are not points in time. Frames are periods of time. It's not even meaningful to use the phrase at frame 1. Saying at frame 1 is like saying at September.
Think of it this way:
Suppose you wanted to walk from New York to Los Angeles over the course of a year. Suppose you set out at the beginning of the first day of winter. Where would you be at winter? At spring? At summer? At fall?
This confusion over how to represent time is why most 3D packages have a "fencepost error" that causes them to handle motion blur in a kludgey way.
Here's a link to an old (pre-blog) web page of mine that develops this motion blur idea further.
The earliest known fence-post error in history?
In the araeostylos [style of temple] it is only necessary to preserve, in a peripteral building, twice the number of intercolumniations on the flanks that there are in front, so that the length may be twice the breadth. Those who use twice the number of columns for the length, appear to err, because they thus make one intercolumniation more than should be used.
- Vitruvius via Robert K. Moniot