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Let's work through another
few scenarios involving

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displacement, velocity, and
time, or distance, rate,

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and time.

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So over here we have, Ben is
running at a constant velocity

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of three 3 meters per
second to the east.

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And just as a review,
this is a vector quantity.

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They're giving us the
magnitude and the direction.

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If they just said 3
meters per second,

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then that would just be speed.

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So this is the magnitude,
is 3 meters per second.

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And it is to the east.

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So they are giving
us the direction.

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So this is a vector quantity.

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And that's why it's
velocity instead of speed.

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How long will it take
him to travel 720 meters.

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So let's just remind
ourselves a few things.

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And I'll do it both with
the vector version of it.

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And maybe they should
say, how long will it

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take them to travel
720 meters to the east,

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to make sure, to make it clear,
that it is a vector quantity.

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So that it's displacement,
as opposed to just distance,

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but we'll do it both ways.

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So one way to think about it, if
we think about just the scalar

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version of it, we said
already that rate or speed

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is equal to the distance that
you travel over some time.

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I might write t there.

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But it's really
a change in time.

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So sometimes some people
would write a little triangle,

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a delta there, which
means change in time.

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But that's implicitly
meant when you just

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write over time like that.

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So rate or speed is equal
to distance divided by time.

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Now, if you know-- they're
giving us in this problem,

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they're giving us the rate.

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If we think about the
scalar part of it,

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they're telling us that
that is 3 meters per second.

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And they're also
telling us the time.

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Or, sorry, they're not
telling us the time.

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They are telling
us the distance,

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and they want us to
figure out the time.

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So they tell us the
distance is 720 meters.

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And so we just have to
figure out the time.

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we So if we just do the
scalar version of it,

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we're not dealing with
velocity and displacement.

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We're dealing with the
rate or speed and distance.

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So we have 3 meters
per second is

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equal to 720 meters over
some change in time.

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And so we can algebraically
manipulate this.

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We can multiply both
sides times time.

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Multiply time right over there.

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And then we could,
if we all-- well,

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let's just take it
one step at a time.

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So 3 meters per second times
time is equal to 720 meters

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because the times on the
right will cancel out

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right over there.

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And that makes sense,
at least units-wise,

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because time is going
to be in seconds,

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seconds cancel out the
seconds in the denominator,

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so you'll just get meters.

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So that just makes sense there.

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So if you want to
solve for time,

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you can divide both sides
by 3 meters per second.

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And then the left
side, they cancel out.

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On the right hand
side, this is going

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to be equal to 720
divided by 3 times meters.

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That's meters in the numerator.

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And you had meters per
second in the denominator.

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If you bring it out
to the numerator,

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you take the inverse of this.

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So that's meters-- let me do
the meters that was on top,

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let me do that in green.

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Let me color code it.

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So 720 meters.

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And now you're dividing
by meters per second.

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That's the same
thing as multiplying

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by the inverse, times
seconds per meters.

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And so what you're
going to get here,

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the meters are
going to cancel out,

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and you'll get 720
divided by 3 seconds.

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So what is that?

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720 divided by 3.

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72 divided by 3 is 24.

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So this is going to be 240.

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This part right over
here is going to be 240.

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And it's going to
be 240 seconds.

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That's the only unit
we're left with,

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and on the left hand side,
we just had the time.

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So the time is 240 seconds.

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Sometimes you'll see it.

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And just to show you,
in some physics classes,

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they'll show you
all these formulas.

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But one thing I really
want you to understand

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as we go through this
journey together,

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is that all of those
formulas are really

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just algebraic
manipulations of each other.

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So you really shouldn't
memorize any of them.

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You should always
say, hey, that's just

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manipulating one of those other
formulas that I got before.

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And even these formulas are,
hopefully, reasonably common

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sense.

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And so you can start from
very common sense things--

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rate is distance
divided by time--

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and then just
manipulate it to get

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other hopefully
common sense things.

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So we could have done it here.

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So we could have multiplied
both sides by time

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before we even put
in the variables,

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and you would have gotten--
So if you multiplied

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both sides by time here,
you would have got,

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on the right hand side, distance
is equal to time times rate,

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or rate times time.

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And this is one
of-- you'll often

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see this as kind of
the formula for rate,

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or the formula for motion.

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So if we flip it around, you get
distance is equal to rate times

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time.

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So these are all
saying the same things.

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And then if you wanted
to solve for time,

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you could divide
both sides by rate,

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and you get distance divided
by rate is equal to time.

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And that's exactly what we got.

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Distance divided by
rate was equal to time.

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So if your distance
is 720 meters,

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your rate is 3
meters per second,

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720 meters divided by
3 meters per second

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will also give you a
time of 240 seconds.

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If we wanted to do
the exact same thing,

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but the vector version
of it, just the notation

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will look a little
bit different.

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And we want to keep track
of the actual direction.

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So we could say we
know that velocity--

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and it is a vector quantity,
so I put a little arrow on top.

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Velocity is the same
thing as displacement.

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Let me pick a nice color
for displacement-- blue.

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As displacement-- Now, remember,
we use s for displacement.

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We don't want to
use d because when

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you start doing calculus,
especially vector

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calculus-- well, any
type of calculus--

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you use d for the
derivative operator.

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If you don't know what that is,
don't worry about it right now.

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But this right here,
s is displacement.

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At least this is convention.

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You could kind of use
anything, but this

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is what most people use.

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So if you don't want
to get confused,

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or if you don't want to be
confused when they use s,

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it's good to practice with it.

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So it's the
displacement per time.

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So it's displacement
divided by time.

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Sometimes, once again,
you'll have displacement

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per change in time,
which is really

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a little bit more correct.

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But I'll just go with
the time right here

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because this is the convention
that you see, at least in most

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beginning physics books.

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So once again, if we
want to solve for time,

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you can multiply
both sides by time.

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And you get-- this cancels
out-- and I'll flip this around.

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Well, actually, I'll
leave it like this.

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So you get displacement
is equal to-- I

167
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can flip these around--
velocity times change in time,

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I should say.

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Or we could just say time
just to keep things simple.

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And if you want
to solve for time,

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you divide both
sides by velocity.

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And then that gives you time
is equal to displacement

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divided by velocity.

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And so we can apply that
to this right over here.

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Our displacement is
720 meters to the east.

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So in this case, our time
is equal to 720 meters

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to the east.

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720 meters east is
our displacement,

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00:07:53,980 --> 00:07:57,140
and we want to divide that
by the given velocity.

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Well, they give us the
velocity of 3 meters

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per second per the east.

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00:08:04,140 --> 00:08:12,470
And once again, 720 divided
by 3 will give you 240.

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00:08:12,470 --> 00:08:15,885
And then when you take
meters in the numerator,

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00:08:15,885 --> 00:08:17,343
and you divide by
meters per second

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00:08:17,343 --> 00:08:19,676
in the denominator, that's
the same thing as multiplying

188
00:08:19,676 --> 00:08:21,790
by seconds per meter,
those cancel out.

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00:08:21,790 --> 00:08:24,440
And you are just left
with seconds here.

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00:08:24,440 --> 00:08:25,860
One note I want to give you.

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00:08:25,860 --> 00:08:28,650
In the last few problems, I've
been making vector quantities

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00:08:28,650 --> 00:08:30,993
by saying to the
east, or going north.

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00:08:30,993 --> 00:08:32,409
And what you're
going to see as we

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00:08:32,409 --> 00:08:35,130
go into more complex problems--
and this is what you might see

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00:08:35,130 --> 00:08:37,730
in typical physics
classes, or typical books,

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00:08:37,730 --> 00:08:39,440
is that you define a convention.

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00:08:39,440 --> 00:08:42,570
That maybe you'll say, the
positive direction, especially

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00:08:42,570 --> 00:08:45,660
when we're just dealing
with one dimension,

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00:08:45,660 --> 00:08:48,500
whether you can either
go forward or backwards,

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00:08:48,500 --> 00:08:49,684
or left or right.

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00:08:49,684 --> 00:08:51,350
We'll talk about other
vector quantities

202
00:08:51,350 --> 00:08:53,280
when we can move in two
or three dimensions.

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00:08:53,280 --> 00:08:55,210
But they might take
some convention,

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00:08:55,210 --> 00:09:00,780
like positive means maybe
you're moving to the east,

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00:09:00,780 --> 00:09:04,890
and maybe negative means
you're moving to the west.

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00:09:04,890 --> 00:09:09,220
And so that way-- well,
in the future, we'll see,

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00:09:09,220 --> 00:09:10,610
the math will
produce the results

208
00:09:10,610 --> 00:09:11,960
that we see a little bit better.

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00:09:11,960 --> 00:09:15,140
So this would just be
a positive 720 meters.

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00:09:15,140 --> 00:09:17,787
This would be a positive
3 meters per second.

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00:09:17,787 --> 00:09:19,870
And that implicitly tells
us that that's the east.

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00:09:19,870 --> 00:09:21,820
If it was negative, it
would then be to the west.

213
00:09:21,820 --> 00:09:22,770
Something to think about.

214
00:09:22,770 --> 00:09:24,978
We're going to start exploring
that a little bit more

215
00:09:24,978 --> 00:09:26,220
in future videos.

216
00:09:26,220 --> 00:09:28,889
And maybe we might say positive
is up, negative is down,

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00:09:28,889 --> 00:09:29,430
or who knows.

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00:09:29,430 --> 00:09:30,888
There's different
ways to define it

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00:09:30,888 --> 00:00:00,000
when you're dealing
in one dimension.