Now we can define instantaneous velocity in analogy to the derivative definition in one dimension eq. 3.3. So we have
Writing this in components gives
Here the subscripts x and y on the velocity denote the components in those respective directions.
So in words, the definition of the velocity vector is
fairly easy to see. It just says to get the x-component of
the velocity, you measure the rate the x-component of position changes in
time. That's what we called 
. The same idea holds for all
the other components.
Again, these are just definitions. They don't contain any physics. We'll see that physical laws are nicely expressed in terms of these definitions and that's why we're defining them the way we are.
