♪♪
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.