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Now that we've described the
displacement of our object--

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remember that our displacement
vector delta r in this time

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interval was x(t) plus
t minus x(t) i hat,

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which we denoted
as delta x i hat.

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Now, let's just remind ourselves
that this distance here, that's

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delta x, and this whole
distance from here

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over to there-- that's what
we mean by x(t) plus delta t.

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And now what we'd
like to do is describe

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what we call average velocity.

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And our average velocity
depends on our time intervals.

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So this is for the
time interval t

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to t plus delta t
while the person has

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displaced a certain
amount of vector delta r.

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And our definition
for v average--

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it's a vector quantity,
so we'll write v average--

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will use three bars to
indicate a definition.

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It is the displacement during
a time interval delta t.

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So, as a vector, we have
delta x over delta t i hat.

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And this component here is
what we call the component

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of the average velocity.

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So this is the component
of the average velocity.

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And, again as before,
this component

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can be positive, zero,
or negative depending

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on the sine of delta x.

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And the key point here
is that average velocity

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depends on whatever time
interval you're referring to.

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So that's our definition
of average velocity.

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And now what we want
to do is consider

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what happens in the limit
as delta t becomes smaller

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and smaller and smaller.

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And that will enable us
to introduce our concept

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of instantaneous velocity.