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i remember reading somewhere, maybe even on this forum, a really simple example that goes a long way to explaining the difference in calculated car lengths from the algebra-style calculation to the real-world (empirical) data. It went something like this:
Q. If two cars were both rated at a 0-60 of 5 seconds exactly how come they don't pull off the line together and stay together all the way to 60?
A. imagine the extreme of the two possible acceleration profiles, ie the first car, car A accelerates from 0-59mph in 1 seconds (remember this is theoretical) and then drives the next 4 seconds as near as damn it 60mph. Now take the second car, car B, whose acceleration profile is the exact opposite. Car B accelerates flat out and gets to 1 mph after 4 seconds, and then from 1 to 60 in the next 1 second. Both cars have a 0-60 time of 5 seconds but clearly car A will have travelled a much greater distance. I won't do the math here but you get the point.
Hope that makes sense, but when I thought about it that way it made such obvious sense that the acceleration profile is so much more important than the 0-60 time. Now obviously no two cars will be as far apart in terms of acceleration profile, but theoretically it makes sense.
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