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00:00:03,490 --> 00:00:05,200
Now that we've chosen
a coordinate system

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00:00:05,200 --> 00:00:07,340
for our runner going
along the road,

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00:00:07,340 --> 00:00:09,710
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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00:00:17,120 --> 00:00:19,420
So let's just imagine
that there is some fixed

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00:00:19,420 --> 00:00:22,540
point in the runner
at the center,

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00:00:22,540 --> 00:00:25,100
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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00:00:28,280 --> 00:00:31,880
to that point, and this
is what we'll refer to

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00:00:31,880 --> 00:00:34,430
as our position function.

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00:00:34,430 --> 00:00:38,570
Now, remember, every point
here has an x-coordinate,

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00:00:38,570 --> 00:00:42,060
so we can now introduce
our position function,

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00:00:42,060 --> 00:00:45,920
which we'll call x of t, which
is the coordinate location

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00:00:45,920 --> 00:00:47,750
with respect to the origin.

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00:00:47,750 --> 00:00:50,830
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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00:00:55,780 --> 00:00:56,910
x(t).

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00:00:56,910 --> 00:00:58,660
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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00:01:05,390 --> 00:01:07,980
to the origin, but
the unit vector

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00:01:07,980 --> 00:01:12,580
is how we describe this as a
vector, and so we write i hat.

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00:01:12,580 --> 00:01:17,660
Now, x(t) is what we call
the component of the position

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00:01:17,660 --> 00:01:19,120
vector.

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00:01:19,120 --> 00:01:23,670
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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00:01:34,960 --> 00:01:37,430
x(t) can also be zero.

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00:01:37,430 --> 00:01:40,539
That's if you're
located at the origin.

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00:01:40,539 --> 00:01:43,539
And if our runner is on the
other side of the origin,

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00:01:43,539 --> 00:01:45,810
x(t) can be negative.

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00:01:45,810 --> 00:01:48,640
So the component of
the position vector

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00:01:48,640 --> 00:01:51,210
can be positive,
zero, or negative,

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and the direction of
the position vector

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00:01:53,970 --> 00:01:57,020
is the sine of the
component times i hat.

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00:01:57,020 --> 00:02:00,550
If the component is negative,
then we have a negative i hat.

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00:02:00,550 --> 00:02:03,510
The position vector is pointing
backwards in the minus x

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00:02:03,510 --> 00:02:04,630
direction.

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00:02:04,630 --> 00:02:08,240
And if x(t) is positive,
positive i hat position

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00:02:08,240 --> 00:02:10,780
vector as shown in
this particular case

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00:02:10,780 --> 00:02:13,910
is in the positive
i hat direction.

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00:02:13,910 --> 00:02:17,440
So that's our first vector,
the position vector,

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00:02:17,440 --> 00:02:19,682
in one-dimensional motion.