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I have trouble interpreting this illustration. I see why r (position) and a (acceleration) are the way they are, but what happened to v? Why is it smaller than its coordinates? Is this another error in my textbook?

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They just wanted to save space, so they drew $\vec v$ as one half of the $\vec v$ they indicated beneath the picture. In the real world, $\vec r$, $\vec v$, and $\vec a$ have different dimensions (units) so one shouldn't draw them to the "same graph" without specifying a convention. They just happened to choose an anomalously different convention for the velocities - by a factor of two. – LuboŇ° Motl Mar 2 '11 at 17:13
Indeed, Lubos is right. The textbook isn't exactly "wrong," but that's definitely not a great diagram. – Colin K Mar 2 '11 at 17:48
Thanks Lubos! If this were an answer I would "accept" it right now. – noname Mar 2 '11 at 18:08
Note that the units of velocity are m/s and those of acceleration are m/s^2, so even the acceleration vector with the "right" length doesn't really fit with the axises. The decision is arbitrary, though a little silly. – dmckee Mar 2 '11 at 18:12
@noname, What textbook is this? – BeauGeste Mar 2 '11 at 19:48

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