WEBVTT
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Now that we've chosen
a coordinate system
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for our runner going
along the road,
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we now want to describe
the position function
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of our coordinate
system with respect
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to our choice of origin.
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Now, the runner is
a non-rigid object.
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Legs and arms are
moving back and forth.
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So let's just imagine
that there is some fixed
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point in the runner
at the center,
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and let's give a vector.
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So we're going to draw a
vector from above our origin
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to that point, and this
is what we'll refer to
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as our position function.
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Now, remember, every point
here has an x-coordinate,
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so we can now introduce
our position function,
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which we'll call x of t, which
is the coordinate location
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with respect to the origin.
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This is a function that
will change in time.
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And our position vector is r(t)
equals the position function
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x(t).
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Now, remember, this is a vector.
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The position function
is just a quantity
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that's describing the location
of this point with respect
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to the origin, but
the unit vector
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is how we describe this as a
vector, and so we write i hat.
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Now, x(t) is what we call
the component of the position
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vector.
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Remember, a vector has a
component and a direction,
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and the component is
the position function.
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And that component
x(t) can be positive,
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as you see in this
particular case.
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x(t) can also be zero.
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That's if you're
located at the origin.
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And if our runner is on the
other side of the origin,
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x(t) can be negative.
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So the component of
the position vector
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can be positive,
zero, or negative,
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and the direction of
the position vector
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is the sine of the
component times i hat.
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If the component is negative,
then we have a negative i hat.
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The position vector is pointing
backwards in the minus x
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direction.
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And if x(t) is positive,
positive i hat position
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vector as shown in
this particular case
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is in the positive
i hat direction.
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So that's our first vector,
the position vector,
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in one-dimensional motion.