Hello and welcome to NinetyEast. In this video we're going to look at distance and displacement.
So distance is something you're probably familiar with already: it's how far something or someone has travelled.
And it's a scalar measurement, so it only has a size (magnitude) associated with it - a number.
Say for example, this is your house. If a friend told you they travelled 2km to get to your house, well that would be the distance
that they travelled. But what you don't know is what direction they came from.
Did they come from the left or from the right?
Who knows?
Displacement on the other hand is a vector measurement; it tells you not only the distance travelled, but also the direction.
So now your friend may say to you that they travelled 2 km
and that they travelled to the west to get to your house.
But there's another aspect of displacement that we need to consider:
displacement takes into account how far something has travelled, in relation to where it started.
That is, it measures the shortest distance between the origin and destination.
So not only do we have a magnitude and direction,
but that magnitude is the shortest distance.
Let's look at an example.
This is your neighbourhood; this is your house,
and this is your friend's house.
Now, your friend is new to the neighbourhood, so when they come to visit you (at least for the first time),
they get a little lost.
The route that they take is not the most direct route.
You on the other hand, when you go to visit your friend (and you take your red car),
you take the most direct route; you know your neighbourhood well.
What's really important to remember is that you're not necessarily taking the most direct route altogether,
but you're taking the most direct route you can using roads.
When you're on your bike however,
and you're using the side paths between roads, you can take the most direct route;
and that is the shortest route between your house and your friend's house.
Let's look at how the distance and displacement compares between all three of these journeys.
So here we've got the map again of our house and our friend's house,
and we've got the three different journeys represented. Blue line = friend's journey. Red line = your journey in your car.
And yellow line = your journey on the bike.
Let's compare the distance first between all three of these journeys. What we know is that your friend travelled 2 km to get to your house.
We're also going to be told that you, having taken a shorter route with your car
only had to travel 1 km to get to your friend's house.
Using your bike however, you managed to reduce this distance to only 800 metres.
Let's compare displacement now.
We've got a compass here that will help us with estimating direction.
We won't get it 100 per cent correct, but we're doing this just to look at the concept of displacement.
If you'd like to make the most of this video, why don't you pause here, have a think about what the displacement would be for every journey,
and join us again to see if you got the same answer.
Remember that displacement has two components to it: first is the magnitude. The origin and the destination are the same for
all three journeys. They may have been swapped depending on who was visiting who,
but the magnitude measurement of displacement will be the same:
it's the shortest distance between the two houses.
Now we need to think about the direction.
When your friend travels from their house to your house,
they're going in a south westerly direction.
So their displacement is 800 metres southwest.
You on the other hand, are moving in a north east direction to meet your friend.
So your displacement in your red car and your yellow bike will be 800 metres northeast.
There's one other aspect of displacement that we need to touch on and that's the same with all vector quantities.
If the origin and the destination are the same,
the displacement will equal zero.
What do we mean by this? Well we know that every 365 days (well 365 + a quarter days),
the earth orbits the sun once.
The distance travelled is really great:
its 940,000,000 km. But because it ends up at the exact same spot that it started at,
the displacement of the earth in those 365 and a 1/4 days is zero.
Ok, so just to review for this video: distance is a scalar measurement,
so it measures magnitude only.
Displacement on the other hand is a vector measurement: it looks at magnitude and direction.
And that magnitude is the shortest distance between the origin and destination.
If the origin and the destination are exactly the same spot, displacement is equal to zero.
We hope that you found this video useful. If you've got any questions, please directly message us through YouTube,
or send us an email to NinetyEastTV@gmail.com.
Thanks everyone!