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- [Instructor] Let's explore
the ideas of position,
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speed, and velocity.
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So let's start with an example.
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We have a car parked here
somewhere on the road.
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What is its position?
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So let's start with that.
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So what is its position?
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Well, the meaning of position
is basically location.
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That's it.
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That's what position is.
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But how do I measure that?
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Well, for that, we need a reference point.
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You always measure the location
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by measuring how far it
is from some reference.
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So for example, let's
choose this as a reference.
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We usually call the reference as a zero,
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or you can call that as an
origin, whatever you want.
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It's not necessary, but
it's convenient to do that.
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And now we can measure this.
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So if you measure this,
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let's say it turns out to be
10 meters, we can now say,
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"Hey, the position of
that car is 10 meters."
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But you can immediately
see one problem with this.
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If I just said the position is 10 meters,
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we wouldn't know whether you were talking
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about 10 meters to the right
or 10 meters to the left.
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And therefore, one way to resolve this
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is to say, "The position is
10 meters to the right," okay?
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But another way to say
that, to say the same thing
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that the position is
10 meters to the right,
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another way to say this is we could choose
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all the markings on the
right side of that origin
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to be positive, and everything else
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on the left side to be negative.
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And so now, we could say
the position of that car
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is plus 10 meters.
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That automatically means
it's 10 meters to the right.
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Now, again, it's not necessary to choose
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a right side to be positive.
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You can choose left side
to be positive as well.
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You're completely free to decide that.
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It's just that it's more of a convention
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to choose right side to be positive.
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And similarly, if the car was parked,
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say, on a vertical track,
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then we would usually choose
upwards to be positive.
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Again, that's a convention,
but we usually do that.
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And now as a result of that, look,
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the position of this car
became minus 15 meter.
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The minus represents it's
below our reference point.
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Anyways, we can go ahead
and write down the position.
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We usually use the letter
X to denote the position.
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But again, you can
choose whatever you want.
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It's more of a convention to do that.
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So in our case, X equals 10 meters.
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You could write plus 10
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to represent that plus
on the positive side.
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But even if you don't write
plus, it's understood.
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So if you don't have
any sign in front of it,
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it already means it's positive.
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But I could have also written
10 meters to the right.
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I could have written 10 meters.
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I would've drawn arrow mark like this.
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All of them represent the same thing.
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But you can see what's important
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is that to represent position,
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you need both the magnitude, 10 meters,
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and the direction as
a sign or you write it
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or you use an arrow mark,
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but you have both magnitude and direction.
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So quantities that have
both magnitude and direction
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are called vector quantities.
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So position is a vector quantity,
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because it requires a direction.
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And we represent that
by using an arrow mark.
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And what's important about
the value of the position is,
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if we had chosen a completely
different reference point,
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let's say we had chosen
our reference point
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to be somewhere over here,
let's say somewhere over here.
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Now look, the position
of that car has changed.
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Even though the car has not moved,
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its new position is minus five meters.
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That's because the
reference point changed.
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So the value, this position value
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depends on where you choose
your reference point.
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Another way of saying this
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is saying that the position
depends on reference frame.
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So it's always important to know
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where you're reference point is,
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which direction you've chosen,
positives and negatives.
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Anyways, coming back now,
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let's make that car actually move.
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Let's say that car moves from
here to here in three seconds.
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Now, we can define a new
quantity called a velocity.
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Velocity is a measure of how quickly
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the position of the car changed.
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And we calculate it as change in position.
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The triangle means delta,
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it means change in position,
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divided by the time taken
for that change in position.
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So in our example, in our example,
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what is the change in position?
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Well, it was here to begin with.
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It went here.
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So from 10 to 25,
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the position has changed by 15 meters.
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How did I get that 15?
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Well, I just did 25 minus 10, right?
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So I did 25 meters minus 10 meters.
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That's the change in position.
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Divided by time taken,
which is three seconds.
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So 25 minus 10 is 15, 15 by
3 is 5 meters per second.
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So what does this number mean?
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Well, first of all, we see
a positive sign over here.
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That means that velocity is to the right,
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and that makes sense.
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The position has changed
to the right side.
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Velocity is also a vector quantity, okay?
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Because position is a vector quantity,
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so velocity becomes a vector quantity.
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So the sign tells you
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which direction the position has changed,
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that the new position is to the right side
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of my initial position.
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And what does the number say?
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Five meters per second.
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It says that if the car was
traveling at a constant rate,
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it would change its position five meters
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to the right every second.
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So if I could see an animation of it,
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this is what it would look like.
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So in the first second,
look, it changed by five.
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And the next second, it changed
again by five to the right.
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And the last second, again,
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it changed by five meters to the right.
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Now, of course you could ask,
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what if the car was not
moving at a constant rate?
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What if it was traveling
a little faster earlier,
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and then it became slower a little later?
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Well, then, this no longer means
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it's traveling exactly
five meters per second.
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Then this would represent
an average value.
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But let's not worry too much about it.
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Okay, let's take one more example.
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Let's say this time, our car goes
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from here to here in five seconds.
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Why don't you figure out
what the velocity is?
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All right, let's see.
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So velocity is, we need to figure out
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the change in position.
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How do we figure out
the change in position?
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Well, it was initially here.
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It finally came over here.
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So changing position is
always final minus initial.
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That's exactly what we
did earlier as well.
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So final velocity.
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Oops, let's use the same color.
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Final position, sorry.
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Final position minus the initial position,
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divided by the time taken for that change.
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And so what will we get?
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Well, this is 5 minus 25 is minus 20.
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Minus 20 by 5 is minus 4.
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So this time, I would get
minus 4 meters per second.
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Again, what does this mean?
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Well, again, the minus sign is saying
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that the velocity of the the position
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has changed to the left over here.
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And that makes sense.
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So we see that, we literally
see the position has changed.
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The new position is to the left side
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of the initial position.
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So that's what the negative sign says.
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But what does four meter per second say?
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Ooh, it's now saying that if the car
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is going at a constant rate,
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the car would now be covering four meters.
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It's changing its position
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four meters to the left every second.
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It's a little slower
than what we got earlier.
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Now, speaking about faster and slower,
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that brings another quantity in our mind
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something that we are
probably familiar with.
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That is speed.
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Well, think of speed as how quickly
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you travel some distance.
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And we calculate speed
as distance over time.
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And again, this would be true if the car
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was going at a constant
speed, but if it was not,
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this would represent the
average speed, just like before.
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But anyways, we can now ask,
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"Well, what's the difference
between speed and velocity?"
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They sound very similar, right?
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Well, let's look at our examples
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one more time and calculate speed.
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Well, in the first case, what's the speed?
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Well, the speed over here was,
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or the average speed, I should say.
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What is the distance traveled?
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Well, the distance
travel is from 10 to 25.
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That is 15 meters
divided by the time taken
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for that distance to be
traveled, that is three seconds.
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And so 15 by 3 is 5.
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I'm getting the same answer as before,
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five meters per second.
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Again, what does this mean?
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This means now the car travels
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the distance of five meters every second,
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that if it was going at a constant rate.
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But if it was not, then
this would represent
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the average value just like before.
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So in general, we just usually call this
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the average speed, okay?
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But this is the same as before.
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So what's the difference
between the speed and velocity?
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Ah, let's look at the second example.
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That will clear things for us.
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So if you go back to our second example
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where the card moved back,
what is the speed now?
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Or what is the average?
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Oops, okay, what is the average speed now?
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Well, the average speed would be
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distance divide by time.
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Again, what is the distance traveled?
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This time, the distance traveled,
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a car came from here to here,
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so the distance traveled is 20.
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Or is it minus 20?
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Well, when it comes to distance,
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I don't care about whether
it's traveling to the left
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or it's traveling to the right.
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All I care about is the
distance, and the distance is 20.
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And that's the key difference.
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So over here, there will
be no negative signs,
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so it'll be just 20 meters
divided by 5 seconds.
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So I get 20 by 5.
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That is just 4 meters per second.
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And you can see there
is no sign over here.
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This means the big difference
between speed and velocity
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is speed only has a magnitude.
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It does not have a direction,
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because distance does
not have a direction.
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I don't care about which
direction it is moving.
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And since speed does not have a direction,
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it is a scalar quantity.
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That's the big difference.
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You can think of speed as
velocity without the direction.
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They both have the same units,
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meters per second as a standard unit,
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or in a more day-to-day life,
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unit would be miles per hour.
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So in short, the big difference
between velocity and speed
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is that when it comes to velocity,
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we care about how much
the position has changed.
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So for example, if the
car started from here,
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went over here, and then
let's say it came back
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to that same position, the
changing position is zero,
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because the car has come back
to the same position, right?
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So as far as velocity is considered,
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there is no change in position.
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But when it comes to speed, speed says,
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"Well, I don't care about
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where your initial and final position is.
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All I care about is how much
distance you've traveled,
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and you have traveled
some distance, right?"
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Distance represents,
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you can think of it as the
odometer reading in your car.
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That number will keep going up, right?
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So you would have traveled some distance,
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and so the distance traveled
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in this round trip would not be zero.
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So you see, velocity is a vector quantity.
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Direction matters.
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But when it comes to speed,
the direction doesn't matter.