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Welcome back.

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I will now introduce you to
the concept of momentum.

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And the letter for momentum is,
in physics, or at least in

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mechanics, it's the letter P.

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P for momentum.

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And I assume that's because the
letter M has already been

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used for mass, which
is I guess an even

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more fundamental idea.

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So P for momentum.

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So what is momentum?

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Well, you probably have
a general idea of it.

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If you see a big guy running
really fast, they'll say, he

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has a lot of momentum.

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And if there's a big guy running
really fast and a

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small guy running really fast,
most people would say, well,

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the big guy has more momentum.

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Maybe they don't have a
quantitative sense of why

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they're saying that, but
they just feel that

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that must be true.

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And if we look at the definition
of momentum, it'll

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make sense.

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The definition of momentum is
equal to mass times velocity.

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So something with, say, a
medium mass and a huge

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velocity is going to have
a big momentum.

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Or something with maybe a medium
mass, but-- the other

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way around.

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I forgot what I just said.

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So medium mass and big velocity,
huge momentum, or

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the other way around.

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Huge mass, medium velocity
would have maybe the same

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momentum, but it would still
have a big momentum.

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Or another way of doing momentum
is how little you

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would like to be in the way of
that object as it passes by.

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How unpleasant would it be
to be hit by that object?

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That's a good way of thinking
about momentum.

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So momentum is mass
times velocity.

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So how does it relate
to everything we've

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been learning so far?

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So we know that force is equal
to mass times acceleration.

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And what's acceleration?

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Well acceleration is just
change in velocity.

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So we also know that force is
equal to mass times change in

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velocity per unit
of time, right?

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Per change in time.

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T for time.

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So force is also equal
to-- well, mass

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times change in velocity.

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Mass, let's assume that
mass doesn't change.

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So that could also be viewed
as the change in mass times

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velocity in the unit
amount of time.

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And this is a little tricky
here, I said, you know, the

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mass times the change in
velocity, that's the same

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thing as the change in the
mass times the velocity,

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assuming the mass
doesn't change.

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And here we have mass times
velocity, which is momentum.

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So force can also be
viewed as change in

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momentum per unit of time.

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And I'll introduce
you to another

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concept called impulse.

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And impulse kind of means
that you think it means.

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An impulse is defined
as force times time.

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And I just want to introduce
this to you just in case you

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see it on the exam or whatever,
show you it's not a

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difficult concept.

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So force times change in time,
or time, if you assume time

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starts at time 0.

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But force times change in time
is equal to impulse.

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I actually don't know-- I should
look up what letters

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they use for impulse.

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But another way of viewing
impulse is force

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times change in time.

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Well that's the same thing as
change in momentum over change

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in time times change in time.

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Right?

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Because this is just the
same thing as force.

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And that's just change
in momentum, so

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that's impulse as well.

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And the unit of impulse
is the joule.

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And we'll go more into
the joule when we do

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work in all of that.

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And if this confuses you, don't
worry about it too much.

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The main thing about momentum is
that you realize it's mass

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times velocity.

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And since force is change in
momentum per unit of time, if

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you don't have any external
forces on a system or, on say,

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on a set of objects, their
combined, or their net

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momentum won't change.

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And that comes from
Newton's Laws.

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The only way you can get a
combined change in momentum is

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if you have some type of net
force acting on the system.

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So with that in mind,
let's do some

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momentum problems. Whoops.

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Invert colors.

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OK.

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So let's say we have a car.

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Say it's a car.

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Let me do some more interesting
colors.

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A car with a magenta bottom.

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And it is, let's see, what
does this problem say?

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It's 1,000 kilograms. So
a little over a ton.

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And it's moving at 9 meters
per second east. So its

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velocity is equal to 9 meters
per second east, or to the

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right in this example.

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And it strikes a stationary
2, 000 kilogram truck.

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So here's my truck.

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Here's my truck and this is
a 2,000 kilogram truck.

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And it's stationary, so
the velocity is 0.

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And when the car hits the truck,
let's just say that it

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somehow gets stuck in the truck
and they just both keep

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moving together.

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So they get stuck together.

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The question is, what is the
resulting speed of the

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combination truck and car
after the collision?

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Well, all we have to do is
think about what is the

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combined momentum before
the collision?

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Well let's see.

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The momentum of the car is going
to be the mass times the

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car-- mass of the car.

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Well the total momentum is going
to the mass of the car

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times the velocity of the car
plus the mass of the truck

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times the velocity
of the truck.

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And this is before they
hit each other.

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So what's the mass of the car?

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That's 1,000.

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What's the velocity
of the car?

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It's 9 meters per second.

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So as you can imagine, a unit of
momentum would be kilogram

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meters per second.

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So it's 1,000 times 9 kilogram
meters per second, but I won't

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write that right now just to
keep things simple, or so I

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save space.

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And then the mass of
the truck is 2,000.

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And what's its velocity?

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Well, it's 0.

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It's stationary initially.

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So the initial momentum of the
system-- this is 2,000 times

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0-- is 9,000 plus 0, which
equals 9,000 kilogram meters

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per second.

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That's the momentum before
the car hits

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the back of the truck.

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Now what happens after the car
hits the back of the truck?

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So let's go to that situation.

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So we have the truck.

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I'll draw it a little
less neatly.

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And then you have the car and
it's probably a little bit--

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well, I won't go into whether
it's banged up and whether it

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released heat and all of that.

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Let's assume that there was
nothing-- if this is a simple

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problem that we can do.

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So if we assume that,
there would be

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no change in momentum.

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Because we're saying that
there's no net forces acting

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on the system.

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And when I say system, I
mean the combination of

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the car and the truck.

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So what we're saying is, is
this combination, this new

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vehicle called a car truck, its
momentum will have to be

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the same as the car and the
truck's momentum when they

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were separate.

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So what do we know about
this car truck object?

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Well we know its new mass.

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The car truck object,
it will be the

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combined mass of the two.

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So it's 1,000 kilograms plus
2,000 kilograms. So it's 3,000

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kilograms. And now we can use
that information to figure out

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its velocity.

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How?

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Well, its momentum-- this
3,000 kilogram object's

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momentum-- has to be the same
as the momentum of the two

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objects before the collision.

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So it still has to be 9,000
kilogram meters per second.

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So once again, mass
times velocity.

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So mass is 3,000 times
the new velocity.

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So we could call that, I don't
know, new velocity, v sub n.

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That will equal 9,000.

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Because momentum is conserved.

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That's what you always
have to remember.

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Momentum doesn't change unless
there's a net force acting on

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the system.

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Because we saw a force is change
in momentum per time.

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So if you have no force
in it, you have

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no change in momentum.

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So let's just solve.

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Divide both sides of this by
3,000 and you get the new

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velocity is 3 meters
per second.

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And that kind of makes sense.

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You have a relatively light
car moving at 9 meters per

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second and a stationary truck.

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Then it smacks the truck
and they move together.

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The combined object-- and it's
going to be to the east. And

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we'll do more later, but we
assume that a positive

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velocity is east. If somehow we
ended up with a negative,

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it would have been west. But it
makes sense because we have

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a light object and a stationery,
heavy object.

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And when the light object hits
the stationery, heavy object,

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the combined objects still keeps
moving to the right, but

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it moves at a relatively
slower speed.

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So hopefully that gives you a
little bit of intuition for

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momentum, and that was not too
confusing of a problem.

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And in the next couple of
videos, I'll do more momentum

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problems and then I'll introduce
you to momentum

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problems in two dimensions.

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I will see you soon.