♪♪
If you're
going on a trip,
you might wanna
know where you are,
where you've been,
and where you're headed.
Thanks to physics,
you have some helpful tools to
keep track of your position.
I'm here in Alexander Park,
in Snellville, Georgia,
 and we're going to use
 this place to talk about
 a couple of those tools,
 called distance
 and displacement.
Let's start with distance.
Distance is a measure of
how far something's traveled.
The SI unit for
distance is meters.
Now, if you
remember in Unit 1,
we talked about the
difference between
scalar and vector
quantities.
Scalar quantities only
have a magnitude,
while vector quantities
have both a magnitude
and a direction.
Distance is a
scalar quantity.
It's only the magnitude of
how far we've traveled.
The direction we moved in
doesn't matter.
 So, let's say Onzer is
 standing on a number line.
 He's starting from 0,
 which we'll call his origin
 or his starting point.
 If he moves 2 meters
 to the right,
 the distance he's
 traveled is 2 meters.
 Now let's say he moves
 4 meters to the left,
 his total distance
 from his origin
 is 2 meters
 plus 4 meters,
 which equals a total
 distance of 6 meters.
 With distance, the direction
 you travel doesn't matter.
So even though he went 4 meters
in the opposite direction,
 the distance will always
 be a positive number.
 Now, what if he walks
 3 meters to the right?
 The total distance he's
 traveled is 9 meters.
 Again, when
 measuring distance,
the path he takes between an
origin and destination matters.
 So, even though he ended up
 only 1 meter away
 from his origin,
 his total distance traveled
 is still 9 meters.
But what if Onzer didn't
want to know the path he took
throughout his journey,
and only cared about
the difference in meters
between his starting point
and ending point?
That's where
displacement comes in.
Displacement is an object's
overall change in position.
Just like distance, the SI unit
for displacement is meters.
Displacement is
a vector quantity,
which means it has a
magnitude and a direction.
So let's go back
to our number line.
 If Onzer moves 2
 meters this way,
 the distance he moves is
 2 meters, just like before.
 But his displacement is
 2 meters to the right.
 Now if he moves 4 meters
 in the opposite direction,
 the total distance
 he's traveled
 since starting
 is 6 meters.
 However, his displacement
 is negative 2 meters.
 So if he moves 3 meters
 to the right, again,
 his distance adds
 up to 9 meters,
 but his displacement
 for the whole journey
 is 1 meter to the right.
So, why is that?
We know our displacement
is the difference in meters
between our initial position
and our final position.
That means the route we took
to get there doesn't matter.
The only thing that matters
is how far we are
from the origin and in
what direction we ended up.
So, his distance
was 9 meters,
but his displacement was
1 meter to the right.
But enough with
number lines.
Let me demonstrate
using a grid.
 Where I'm standing right now
 is my starting point,
 or my origin.
 On this grid, north is up,
 west is to the left,
 south is down,
 and east is to the right.
 Let's call the origin
 point A on the grid.
 I'm going to move 4 meters
 to the right, or eastward,
 to what we can
 call point B.
 Next, I'm going to move
 3 meters north,
 to what we can
 call point C.
 The total distance I traveled
 since I left point A
 is 4 meters
 plus 3 meters,
 which is a total of 7 meters
 to get to point C.
 With distance, we only
 need to know the route
 that we took to go from our
 origin to our destination.
 But with displacement,
 we only need to know the
 origin and destination,
 and the shortest route
 between the two points.
 In my case, my displacement
 is how far point C is
 from point A if we drew a
 straight line between them.
Knowing that, we can
figure out the displacement.
 This looks like a job for
 the Pythagorean Theorem.
 The equation,
 if you remember,
 is A squared plus B squared
 equals C squared.
 A is the distance AB,
 which is 4 meters.
 B is the distance BC,
 which is 3 meters,
 and C is the distance AC,
 which is our displacement.
 If we plug everything in,
 we see that 4 squared plus 3
 squared is equal to C squared.
 So 16 plus 9 is
 equal to C squared.
 Hence, C squared
 is equal to 25.
 If we take the square root
 on both sides,
 we find out that C is
 equal to 5 meters.
 So, even though the distance
 we traveled in our journey
 from A to C
 is 7 meters,
 our displacement
 is 5 meters.
 Remember, displacement
 is a vector quantity,
 so it has both magnitude
 and direction.
 So our displacement is
 actually 5 meters northeast.
 To summarize, distance
 is a scalar quantity.
 It's the magnitude in
 meters of the path
 an object takes from its
 origin to its destination.
 Displacement is
 a vector quantity.
 It's the difference
 in meters between
 an object's origin
 and destination,
 and the direction
 it occurred in.
These differences will start
becoming very important
when we start to calculate
motions of objects
in later segments.
That's it for this segment
of "Physics in Motion",
and we'll see
you guys next time.
 For more practice problems,
 lab activities,
 and note-taking guides,
 check out the
 "Physics in Motion" Toolkit.
