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 
equals 15 miles, and
our initial time 
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 
equals 75 miles, and our final time 
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 
. It is the ratio of the change in position 
, to
the change in time 
.
Often as a shorthand, we'll write 
, and
. So the Greek letter 
can be thought
of as meaning "the change in". In this way, our definition
of average velocity can be written more succinctly as 
.
