Now that we've described the displacement of our object--
remember that our displacement vector delta r in this time
interval was x(t) plus t minus x(t) i hat,
which we denoted as delta x i hat.
Now, let's just remind ourselves that this distance here, that's
delta x, and this whole distance from here
over to there-- that's what we mean by x(t) plus delta t.
And now what we'd like to do is describe
what we call average velocity.
And our average velocity depends on our time intervals.
So this is for the time interval t
to t plus delta t while the person has
displaced a certain amount of vector delta r.
And our definition for v average--
it's a vector quantity, so we'll write v average--
will use three bars to indicate a definition.
It is the displacement during a time interval delta t.
So, as a vector, we have delta x over delta t i hat.
And this component here is what we call the component
of the average velocity.
So this is the component of the average velocity.
And, again as before, this component
can be positive, zero, or negative depending
on the sine of delta x.
And the key point here is that average velocity
depends on whatever time interval you're referring to.
So that's our definition of average velocity.
And now what we want to do is consider
what happens in the limit as delta t becomes smaller
and smaller and smaller.
And that will enable us to introduce our concept
of instantaneous velocity.