Lesson video

Hello there, I'm Mr. Forbes and welcome to this lesson from the Measuring and calculating motion unit.

The lesson's called displacement and velocity of vectors.

And in it we're going to see what displacement and velocity are and compare them to the quantities you may already know, distance and speed.

We'll be seeing how to combine displacements together to get an overall displacement.

And we're also gonna be seeing what happens when objects move in circles.

By the end of this lesson, you're going to be able to calculate the velocity of moving objects.

You're also going to be able to compare velocity with speed so that you understand the difference between those two.

And you're going to be able to describe the motion of an object in a circle.

There are just three keywords that you need to know for this lesson.

The first of them is displacement, and the displacement is the distance an object is from its starting point.

The second keyword is vector.

And a vector quantity is a quantity that's got a size of magnitude and a direction associated with it.

And third, velocity.

And as you'll find out in this lesson, velocity is a speed in a particular direction.

And here's the definitions of those keywords.

And it can return to this slide at any point during the lesson.

The lesson's in three parts.

And in the first part, we're going to be concentrating on displacement and comparing that with distance.

And in it we'll see that displacement is distance in a particular direction from a starting point.

In the second part, we're gonna move on to look at velocity and we'll see that that speed in a particular direction.

And in the final part, we'll look at situations involving average velocity and find out about that.

We'll also look at motion of objects travelling in circles.

So, when you're ready, let's start with the first bit, displacement.

As I said, we are gonna start this lesson by looking at displacement and compare it to the distance travelled.

So what I've got here is a map of the British Isles and on it I've marked John o' Groats and Land's End.

And they're opposite ends of Great Britain, the largest of the islands.

If you drove between those two points, you'd follow a path something like this.

And the shortest distance you can travel by road is about 1,400 kilometres.

But if you could fly in a straight line between those two points from John o' Groats straight down to Land's End, that distance would only be a distance to about 970 kilometres.

So that those two distances are different.

One of them is a straight line distance and one of them is the shortest distance you could actually take travelling across the land.

So in either case, you'd finish your journey 970 kilometres from your starting point roughly south.

So, there are two different measurements you could take moving between those two points.

You could measure the distance that how far you've travelled across the land through the roads, and that would give you 1,400 kilometres or you could measure how far you are from the actual starting point in a straight line.

And that's a different distance.

That's 970 kilometres.

And it's also in a specific direction.

It's roughly south as the starting point.

So there's two different measurements there.

Distance and displacement.

So the displacement is a measurement of how far you are from a starting point, but also in what direction you are.

And it's a straight line.

So these type of quantities are called vectors or so a vector quantity as direction and also magnitude or size.

And whenever you're specifying a vector, you need to specify the direction, otherwise you're not actually giving a full answer.

So, I've got two journeys here from point A to point B and point C, and both of those distances are two metres.

As you can see, if I didn't specify the direction, I could end up at any of those point B or C from A.

So I need to specify the direction whenever I'm writing down a vector like displacement.

Okay, first to check if you're understanding here, which of those measurements there are displacements? And you can choose more than one.

So pause the video, make your selection, and then restart.

Okay, welcome back.

And you should have chosen the ones that have got distances and directions.

So four kilometres west and 60 centimetres to the left.

Both of those have distances and directions.

Well done for selecting those.

Let's have a more detailed look about what I mean by displacement.

Our position is here.

She's got a displacement three metres to the left of Lucas.

So I'm comparing her position to him, but I can do that comparison the other way around.

I can also say that Lucas has a displacement three metres to the right of Izzy.

I can also use map directions in my descriptions of displacement.

So from Belfast to Edinburgh, that's 230 kilometres in the northeast direction as I've shown by an arrow there.

If I move from Cardiff to Edinburgh, that's 500 kilometres north.

So the displacement is 500 kilometres north.

And if I move from Liverpool to London, I'd be travelling 290 kilometres to the southeast.

So I can use left right map directions or up and down to specify the direction involved in a displacement.

So let's check your understanding of displacement.

Again, if you travel from John o' Groats to Land's End and back to Land's End again, your final displacement is zero.

And I've mapped those two points on the map there for you.

So, is that true or false? So pause the video, make the decision, and restart.

Okay, welcome back.

You should have selected true there, your final displacement is zero, but what I'd like you to do is to explain the answer.

So I'd like you to read through both of those and select one of them.

So pause the video, make your selection, and then restart.

Okay, welcome back.

Well, you should have chosen answer A, the distance away from your starting point is zero.

You're back exactly where you started.

Well done if you selected those.

As you've already seen, the distance you travel moving between points is not the same as the displacement.

So if I travel that distance between points A and B, I'll travel quite a long distance.

I could do a slightly shorter distance if I travel along that route.

This route would be a bit longer because I'm zigzagging over the place.

And in this one I'm doing a bit of a loop backwards.

So I travel a different distance again.

So all of those distances are different, but the displacement is this line here, is the direct shortest distance between the two points in a straight line.

So distance and displacement are very different things even though they're both measured in metres.

Let's check if you understand the difference between distance and displacement here.

So I'll run a complete one lap of a 400 metre track and reaches the start line again, which of these statements are correct.

And I'd like you to select two of these.

So pause the video, make your selection, and restart.

Okay, welcome back.

Well, they went around a complete lap.

So the distance they travelled was 400 metres.

They actually ran 400 metres, but they're exactly where they started.

So their final displacement is zero metres.

So well done if you selected those two.

Now, it can be awkward when you're trying to describe displacement and you've got to put in northeast, northwest, southeast, and things like that.

So we often describe displacement as positive and negative numbers because we are only analysing situations where objects move along a straight line.

So I've got a straight line here and if I wanted to describe displacement, I could put some positive displacement marks on one side of it and negative displacement marks on the other.

So to the right I'm saying is positive displacement here and to the left negative displacement.

So if I placed Jacob above there, he's got a displacement of plus three metres because he's on the positive side of the line.

Alex is four metres.

But on the other side of the line, if I place Lucas, he's on the negative side.

He's to the left there.

So he's got a displacement of minus three metres.

He's three metres from the starting point in the negative direction.

And Izzy there at minus five metres.

So using positive and negative numbers is the simplest way to describe displacement.

Let's do another check about displacement and distance.

A pupil walks a distance of one metre in a straight line and then walks another one metre in a straight line.

The displacement must be two metres from the starting point.

Is that true or is that false? So pause the video, make your selection, and restart please.

Welcome back.

That's false.

It doesn't have to be two metres, but why is that? I'd like you to have a look at those two options and select one of them.

So pause the video, select, and then restart.

Okay, and the reason that the displacement doesn't have to be two metres is because they could have changed direction at any point.

They could have had displacement of up to two metres or down to zero metres 'cause they could have just walked back to where they started from.

So well done if you selected that.

Now, we can compare distance and displacement in a bit more detail.

So I've got a number line here and I'm going to position someone on the line.

And I've decided that backwards are negative directions there and forwards is to the right there.

And I'm gonna look at movement, the total distance they've travelled and the displacement.

So the first type of movement to do is they walk forwards two metres.

So the distance they've travelled is two metres.

And you can see from the diagram, their displacement is plus two metres.

The two metres in the forwards direction from the starting point.

And if I instruct them to walk forwards, one more metre, a total distance they've travelled has gone up by one metre.

It's three metres, and their displacement is plus three metres.

But now, I give them the instruction to walk backwards five metres.

So she's walked backwards five metres there.

Her distance travelled is increased by five metres.

She's five more metres, but her final displacement is now minus two metres.

So we've taken the direction of travel into account there to get a final displacement of minus two metres.

So you can see the distance travel and the displacement are not the same.

Let's have another comparison of displacement and distance.

So again, I've got my number line here and we start in the centre.

Displacement, zero, and distance travelled, zero.

I've got my left and right is positive and negative there.

So my first instruction move right four metres.

Distance travelled is four metres.

Displacement is four metres.

Then if I move left nine metres, well, I've moved a total of four plus nine.

That's 13 metres.

But my displacement, I've gotta take into account that direction again.

So I'm subtracting that nine metres to the original four.

I'm at minus five metres as you can see.

And finally I move right five metres.

I've travelled a total distance of 18 metres, but my final displacement is zero metres.

I've ended up exactly where I started.

So let's try and work out some final displacement and distances now.

I'll do one and then you can have a go.

So I've got Izzy walking six metres north, then four metres south and five metres north again.

What's the total distance travelled and her displacement from the starting position? So to find the distance travelled, all I have to do is add together all the separate distances so that they are added together.

She's walked 15 metres.

Then to find her displacement, what I've gotta do is decide which way is positive and which way is negative.

So I'm gonna use north as the positive direction.

And my final displacement then is six metres north minus four metres because she's moved south plus five metres north again.

And that gives me a final displacement of seven metres north.

Now, it's your turn.

I'd like you to find Jun's position please.

So the total distance travelled and displacement from the starting position.

Pause the video then restart when you're done.

Okay, welcome back.

Well, adding together all the distances should give you a value of 21 metres.

He's moved 21 metres.

And if you used west as positive, then your final displacement there of plus three metres west.

If you chose an east as positive, you'll find that you've got minus three metres east as an answer.

Both of those would be correct.

Well done if you've got that.

Okay, it's time for the first main task of the lesson.

And what I'd like you to do is to read the passage there and complete it by adding the words distance and displacement to it.

Only those words.

Obviously, you'll have to use them more than once each.

So pause the video, fill in those gaps, and then restart please.

Okay, welcome back.

Well, you should have filled in these answers.

When an object moves, distance is a measure of how far it's travelled along its path.

The direction it's travelled doesn't matter.

The length of a line drawn from the starting point to the end of the journey together with a direction from start to finish is called the displacement.

Distance is a scalar quantity.

It's only got magnitude, only got size.

Displacement is a vector quantity.

It's got magnitude and direction.

And when writing down a displacement, you must give both the magnitude and the direction from the starting point.

Well done if you've got those answers.

Okay, it's time to move on to the second part of the lesson.

And this is all about velocity.

As you'll see in it, velocity is a vector as well.

So, let's get started.

The velocity of an object is its speed in a particular direction.

So you specify its speed and you also specify the direction of travel.

It's a vector quantity like displacement was.

So you can have velocities like this.

You might be running five metres per second left.

So you've specified the speed and the direction of travel there.

You might be travelling 100 metres per second up if you are in a rocket.

You could be sailing five kilometres per hour west.

So you can give any unit speed and any direction to specify the velocity of the object.

Unlike velocity, some quantities don't have directions associated with them.

They're scalar quantities and you've come across quite a few scalar quantities already.

So scalar quantities have magnitude.

They have size.

They can be added or subtracted easily.

So if you get five kilogrammes and then another five kilogrammes, you can just simply add those together.

You've got no direction so you don't have to worry about that.

So examples of scalars are speed, mass, distance.

Vectors on the other hand have magnitude and direction.

And you have to take into account that direction when you're trying to add them together.

So when you're combining vectors, you need to be very careful about the directions.

And they're represented by arrows commonly on diagrams. Examples you've seen already, velocity and displacement, with forces and acceleration, which you'll see in other lessons, are also vectors.

As I've said, with any vector, you need to take into account the direction.

So the direction of travel must be included with a velocity.

So I've got a car here, car A.

It's got a velocity of six metres per second to the right and I've shown that by the arrow there.

I've got a second car here and its velocity is six metres per second to the left.

Those cars have the same speeds but they've got different velocities so they're going in different directions.

So they have different velocities.

Just as with displacement, you can represent velocities using positive and negative numbers.

So this green car, it's travelling at six metres per second.

I could say it's got a velocity of plus six metres per second.

I'm taking travelling to the right as being positive in this case.

This red car, it's travelling at six metres per second, so its speed is six metres per second, but its velocity, because it's travelling in the opposite direction, would be represented by minus six metres per second.

Third car here is travelling towards the right, positive velocity, and a fourth car here travelling towards the left and therefore a negative velocity.

So I can just specify velocities in straight lines by using positive and negative numbers.

Okay, it's time for us to see if you understand the difference between vectors and scalars.

What I'd like you to do is to pause the video, read that paragraph, and fill in one word answers to each of those gaps, a, b, and c please.

So pause, fill in the answers, and then restart.

Okay, welcome back.

Well, filling in the answers, the scalar quantity distance divided by time gives speed.

That's only got magnitude.

It's a scalar quantity.

The vector quantity displacement divided by time gives velocity.

That's got a magnitude and a direction.

And when you write down a velocity, you should give both the magnitude and the direction.

And there's an example of velocity.

Well done if you've got those.

We can find a velocity of an object using the speed equation but using displacement instead of distance.

So the equation would then be velocity is displacement divided by time or v equals s divided by t.

For displacement, we use the symbol s that's measured in metres.

Velocity v is metres per second and time t is measured in seconds.

But we must remember to include the direction of movement as well.

Okay, let's see if we can use that equation to calculate some velocities.

I'll do one and then you can do one.

So I've got a car travelling 500 metres north in 25 seconds.

Calculate the velocity of the car.

I write out the equation.

I substitute in the final displacement and the time there and I do that calculation.

It's moving 20 metres per second, but that's just the speed I need to also put in the direction.

So direction is north.

Now, you can have a go.

Got a bicycle travelling 60 metres to the left in eight seconds.

Calculate the velocity of the bicycle.

So pause the video, do your calculation, and restart please.

Welcome back.

Well, your solution should be like this.

The equation, put in the values, and that gives you a final velocity of 7.

5 metres per second to the left.

Well done if you've got that.

One last check here to see if you understand how to calculate velocity.

An eagle flies northeast from its nest, it flies 600 metres in 50 seconds.

What's the velocity of the eagle? So which of those calculations is the correct one? Pause the video, make your decision, and then restart please.

Okay, welcome back.

You should have chosen 12 metres per second northeast.

Well done if you've got that.

Okay, now it's time for the task.

And what I'd like you to do is to compare scalar and vector quantities.

I'd like you to fill in these two diagrams, giving me the definitions of each, a scalar and a vector.

Then give me any facts you know about scalars and vectors.

Give me some examples or list any examples you saw in this lesson or other lessons.

And then you give me some things that people might confuse for scalars and vectors which aren't.

So what I'd like you to do is to fill in those two diagrams for me please.

So pause the video, fill them in, restart.

Okay, welcome back.

Your diagram for scalar quantities should look something like this.

A definition, something to do with having magnitude and no direction.

Some facts about them, you could add them together very simply, like the mass I've got there.

There's a set of six examples I found: speed, distance, power, mass, energy, and time.

And here's a set of things that are not scalars.

These are all vectors in fact.

Well done if you've got something like that.

And for your second diagram about vectors, your definition should be something like this.

It's got magnitude and direction.

Some facts about it.

You can represent them as positive and negative values along straight lines, but you need to be very careful about the direction we're adding them together.

The examples are velocity, displacement that we'll see in this lesson, momentum, force, and acceleration.

You'll see elsewhere and non examples, well these are all some scalars.

So well done if your diagram looks anything like that.

Now, it's time to move on to the third and final part of the lesson, which is about finding average velocities for things that are moving.

But also we're gonna just look at things moving in a circle.

The average velocity of something is often confused with average speed and it's not the same thing.

To give you an example for that, well, let's have a look at this scenario here.

So we've got four people and they're gonna walk from A to B and they're gonna all walk at the same speed as each other.

So here's the first person, following that big curve path there.

The second person, slightly shorter path.

Third person's zigzagging.

And a final person, they loop around a bit in the middle there.

Each of those four people are travelling different distances.

And if they're travelling at the same average speed, that means they're gonna arrive at point B at different times.

The time to take and to reach point B is gonna be different for each of those four people.

So the average velocities, 'cause they've all ended up the same displacement from the starting point, they've all got different times, their average velocities are all going to be different in each other even though their average speeds were all the same.

So you can check the difference between average speed and average velocities here.

What I'd like you to do is answer this question.

Got Lucas travelling in a straight line from X to Y in 16 seconds and Andeep's travelling along the red path.

It takes 20 seconds.

I'd like you to calculate their average speeds and their average velocities please.

And you've got the distances they travel mapped on the diagram.

So pause the video, do those calculations, and restart please.

Welcome back.

Well, if you completed the table, you should have got results like this.

And as you can see, because Lucas went in a straight line, his average speed and average velocity are the same.

But because Andy wandered around a little bit in his journey, he's got an average velocity that's lower than his average speed.

Well done if you've got those.

So even if you travel along a straight line, average velocity and average speed aren't necessarily the same.

They can be very different values.

So we've got another movement line here.

We're gonna start at zero and we're gonna compare average speed and average velocity.

So in the first part of the movement, it move forwards two metres in four seconds.

So we can find the average speed there.

It's not 0.

5 metres per second and the average velocity will be the same.

Again, we walk forwards five metres in three seconds.

Find the average speed and the average velocity.

They're still the same because we've moved just in one direction.

But now, if we move backwards two metres and three seconds, we can calculate the average speed again here.

We've got total time taken and the total distance that gives north 0.

9 metres per second.

But the average velocity, because we're using a displacement, it's gonna give us a different value.

That's only north 0.

5 metres per second.

So average speed and average velocity are not the same.

Okay, a bit of a challenging check for you here.

I've got another description of Sophie walking and what I'd like you to do is to decide which two of those statements are correct and you'll have to do some calculations for that.

So pause the video, do those calculations, and select the correct two please.

Welcome back.

Hopefully you selected these two.

Her average speed is north 0.

8 metres per second and her average velocity is north 0.

6 metres per second forwards.

Being very careful there to specify a direction.

The mathematics you needed to do there is there.

Distance and displacement are different in this example.

So we get different speeds and velocities.

Well done if you got those.

So far we've just looked at objects that move in straight lines, but objects can move in other paths as well.

Quite often they can move in circles.

So the International Space Station orbits around the Earth in a circular path, bit like this shown by the pink dotted line there.

And it travels at a constant speed and that's quite high speed.

It's about 7.

7 kilometres a second.

So every second it travels 7.

7 kilometres.

Its speed is constant for it to move in that circular path, but its direction of travel is constantly changing.

As it goes around in a circle, it stays at the same speed but it travels in different directions.

It's instantaneous velocity.

The velocity at any particular moment must be changing 'cause it's moving because even though its speed is staying the same, its direction of travel is changing all the time.

So the instantaneous velocity of any object moving in a circle is constantly changing even though its speed is constant.

The direction of travel is constantly changing.

You're moving in different directions, north, south, east, or west.

The velocity is changing all the time, but the average velocity for a complete lap must be zero because the final displacement after completing a circle is zero.

So you're getting a difference between instantaneous velocity and average velocity there.

Let's see if you understand a bit about circular motion.

I've got the Moon orbiting the Earth in a circular path at a speed of one kilometre per second roughly.

Which of these statements are true? So which two? So pause the video, read those, and select two please.

Welcome back.

You should have chosen these two.

The instantaneous velocity is changing as it moves and the direction that Moon travels is changing during the orbit as well.

It's constantly changing direction, so it's constantly changing velocity.

Well done if you chose those two.

Okay, time for the final task of the lesson here.

I've got a car.

It travels around a bend at a steady speed.

It takes the car five seconds to move from position X to position Z.

And I'd like you to explain why the velocity of the car has changed but the speed is not.

I'd like you to work out the average speed of the car around the bend.

I'd like you to work out the magnitude of the size of the average velocity of the car.

And I'd like you to draw an arrow to indicate the direction of the average velocity on the diagram please.

So pause the video, work out those, and then restart.

Okay, welcome back.

Well, the answer to the first of those is shown here.

The direction of travel has changed.

So the velocity must be different because the direction of movement has changed.

Well done if you've got that.

And here are the solutions to the other three parts of the question.

The average speed is 12 metres per second.

The magnitude of the average velocity is 11 metres per second.

And you can see I've drawn a red arrow there to show the direction of the average velocity.

Well done if you got those.

Okay, we've reached the end of the lesson now, and here's a summary of the information you should have learned.

Displacement is a vector that represents the distance away from a point and the direction.

So how far you are and in what direction.

Velocity is a vector that represents the speed in a particular direction as well.

And if we're analysing motion along the straight line, we can use positive and negative values for displacement instead of having to specify specific directions.

The instantaneous velocity of anything travelling in a circle is always changing, even if its speed isn't.

Well done for reaching the end of the lesson.

I'll see you in the next one.