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Now that we've described the
position vector of the runner,

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00:00:06,510 --> 00:00:08,540
let's try to describe
what happens in time

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00:00:08,540 --> 00:00:10,510
as a runner moves
along our road.

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00:00:10,510 --> 00:00:15,480
Suppose at a later time our
runner has gone down the road

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just a little bit.

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00:00:17,000 --> 00:00:21,060
And so the runner has
moved a little bit.

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Remember, at time t, we
described the position vector

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r(t) was equal to the
coordinate function

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00:00:31,060 --> 00:00:34,070
x as a function of time i hat.

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00:00:34,070 --> 00:00:38,060
And this distance
here was our x(t).

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00:00:38,060 --> 00:00:41,530
Now, our position vector
a little bit later.

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00:00:41,530 --> 00:00:45,570
So here we are at
time t plus delta t.

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00:00:45,570 --> 00:00:47,430
The runner has
moved a little bit.

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00:00:47,430 --> 00:00:50,380
And we'll now describe
the position vector--

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00:00:50,380 --> 00:00:52,570
because I don't
want to overlap it--

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that center point is up here.

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00:00:54,670 --> 00:00:57,260
It's going to point
in this direction.

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00:00:57,260 --> 00:01:01,950
And this is what we
call r(t) plus delta t.

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00:01:01,950 --> 00:01:05,830
In that vector,
r(t) plus delta t,

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the coordinate function
is no longer at time t

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but t plus delta t i hat.

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00:01:12,880 --> 00:01:14,720
And we would now
like to describe

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the displacement vector.

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00:01:16,620 --> 00:01:23,520
So our next step is to describe
the displacement vector

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00:01:23,520 --> 00:01:28,890
for the interval t
to t plus delta t.

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00:01:28,890 --> 00:01:32,300
And that displacement vector
is defined-- we use the symbol

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00:01:32,300 --> 00:01:37,280
delta r, and what we
mean is the vector r(t)

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plus delta t minus
the vector r(t).

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00:01:41,750 --> 00:01:44,940
Now, what that
vector corresponds to

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is the vector right here.

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This is our delta r.

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00:01:50,130 --> 00:01:53,850
And if we now use our
two definitions here,

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then this becomes x(t) plus
delta t minus x(t) i hat.

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00:02:04,030 --> 00:02:09,100
And this quantity here we
refer to as the component

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00:02:09,100 --> 00:02:12,270
of the displacement vector.

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00:02:12,270 --> 00:02:21,530
So delta x is the component
of the displacement vector.

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00:02:24,290 --> 00:02:29,450
And as before, the
component can be positive,

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which would correspond
to the person moving

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a positive component,
positive i hat direction,

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00:02:35,540 --> 00:02:39,180
in the positive x direction
as shown in this figure.

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If the displacement
of vector is zero,

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the person could
have run forward

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and come back and at
time t plus delta t

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be in exactly the
same spot as time t.

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The displacement vector
is zero in that case.

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00:02:54,240 --> 00:02:57,060
The displacement
vector could have

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a component that's negative.

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00:02:59,430 --> 00:03:02,600
And what negative means is at
the end of this interval-- t

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00:03:02,600 --> 00:03:08,460
plus delta t-- that the person
is to the left of the runner.

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00:03:08,460 --> 00:03:11,250
And so this quantity
would be negative.

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00:03:11,250 --> 00:03:14,470
And so this is our crucial
displacement vector that

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describes only the difference
in positions between the person,

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between time t plus
delta t, and time t.