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Average velocity

Suppose you're cruising down the highway and you go 60 miles in 1 hour. Then your average velocity is 60 mi/hr. Now we are going to go through this more formally as follows. Say we measure everything along a line from point. That is we were driving along a straight road and we had set our odometer to zero in San Jose. Now it reads 15 miles, and we look at our clock and it says that it's 9 A.M.. Introducing variable names to describe this, our initial position tex2html_wrap_inline1352 equals 15 miles, and our initial time tex2html_wrap_inline1354 equals 9 hours Later on we look at the odometer and it reads 75 miles, and our clock reads 10 AM. So we can introduce two other sets of variables to describe this. Our final position tex2html_wrap_inline1356 equals 75 miles, and our final time tex2html_wrap_inline1358 equals 10 hours.

Why bother to go to all the trouble of inventing four variable names? It seems like a pretentious way of saying something quite simple. Well the reason is that physics is much easier dealt with in terms of mathematical equations. If we can translate everyday happenings into a precise mathematical formulation, then we'll see that it's possible to do pretty amazing things! So just put up with this for the moment, and later on you'll see that it is indeed quite useful.

So now we are in a position to define the average velocity in one dimension tex2html_wrap_inline1360 . It is the ratio of the change in position tex2html_wrap_inline1362 , to the change in time tex2html_wrap_inline1364 .

  equation115

Often as a shorthand, we'll write tex2html_wrap_inline1366 , and tex2html_wrap_inline1368 . So the Greek letter tex2html_wrap_inline1370 can be thought of as meaning "the change in". In this way, our definition of average velocity can be written more succinctly as tex2html_wrap_inline1372 .


next up previous
Next: Instantaneous velocity Up: Definition of velocity Previous: Definition of velocity

Joshua Deutsch
Mon Jan 6 00:05:26 PST 1997