Lesson video

Hello there, my name is Mr. Forbes and welcome to this lesson from the Measuring and Calculating Motion Unit.

This lesson's all about displacement and velocity.

We're gonna find out that those two quantities are vectors and compare them with distance and speed, quantities that are very similar.

We'll be looking at how to combine different movements to find overall displacement from a starting point.

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

You are also going to be able to compare velocity and speed so that you understand the difference between those two.

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

The first of them is displacement, and 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 or magnitude and a direction associated with it.

And third, velocity.

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

And here's the definitions of those keywords, and you can return to this slide at any point during the lesson.

The lesson's in three parts.

And in the first part, we're gonna concentrate on displacement.

We're gonna find out that displacement is a distance in a particular direction from a starting point.

In the second part of the lesson, we'll move on to velocity and see how that's speed in a particular direction.

And in the final part, we'll look at situations where we can analyse the average velocity of a moving object.

So when you're ready, let's get on with the first part and look at displacement.

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

So what I've got here is the map of the British Isles and on it I've marked John o'Groats and Land's End, and they're at 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 of about 970 kilometres, so 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, 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 of 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 and so a vector quantity has direction and also magnitude or size.

And whenever you specify 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 2 metres.

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

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

Okay, first check of your 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.

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

So 4 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.

I positioned Izzy here, she's got a displacement 3 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 3 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 a north-east direction, as I've shown by the 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 south-east.

So I can use left right map directions, or up and down to specify the direction involved in the 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 marked those two points on the map there for you.

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

Okay, welcome back.

You should have selected true there.

Your final displacement is zero.

And 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 all 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 those distances are different, but the displacement is this line here, it's 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 a runner completes 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 complete laps, 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 north-east, north-west, south-east and things like that, so we often describe displacements 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 displacements, 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 place Jacob up there, he's got a displacement of +3 metres, because he's on the positive side of the line.

Alex is 4 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, do he's got a displacement of -3 metres.

He's 3 metres from the starting point in a negative direction and Izzy there at -5 metres.

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

Let's do another check about displacement and distance.

A pupil walks a distance of 1 metre in a straight line and then walks another 1 metre in a straight line.

Their displacement must be 2 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 2 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 restart.

Okay, the reason that displacement doesn't have to be 2 metres is because they could have changed direction at any point.

They could have had displacement of up to 2 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 gonna position someone on the line and I've decided that backwards and 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 they do is they walk forwards 2 metres.

So the distance they've travelled is 2 metres and you can see from the diagram, their displacement is +2 metres, they're 2 metres in the forwards direction from the starting point.

And if I instruct them to walk forwards one more metre, the total distance they've travelled has gone up by one metre, it's 3 metres, and their displacement is +3 metres.

But now I give them the instruction to walk backwards 5 metres.

So she's walked backwards 5 metres there.

Her distance travelled has increased by 5 metres, she's done 5 more metres, but her final displacement is now -2 metres.

So we've taken the direction of travel into account there to get a final displacement of -2 metres.

So you can see the distance travelled 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 as positive and negative there.

So my first instruction move right 4 metres, distance travelled is 4 metres, displacement is 4 metres.

Then if I move left 9 metres, well I've moved a total of 4 plus 9, that's 13 metres, but my displacement, I've got to take into account that direction again.

So I'm subtracting that 9 metres from the original 4.

I'm at -5 metres as you can see.

And finally I move right 5 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 6 metres north, then 4 metres south and 5 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 there they are, added together, she's walked 15 metres.

Then to find the displacement, all I've got to 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 6 metres north, minus 4 metres, because she's moved south, plus 5 metres north again, and that gives me a final displacement of 7 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 +3 metres west.

If you chose an east as positive, you'll find that you've got -3 metres east as an answer.

Both of those would be correct.

Well done if you 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 has travelled along its path.

The direction its travels doesn't matter.

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

Distance is a scale of 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, and 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 5 metres per second left, so you've specified the speed and the direction of travel there.

You might be travelling a hundred metres per second up if you're in a rocket.

You could be sailing 5 kilometres per hour west.

So you can give any unit of 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 5 kilogrammes and then another 5 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.

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, but 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 6 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 6 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 6 metres per second.

I could say it's got a velocity of +6 metres per second.

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

This red car, it's travelling at 6 metres per second, so its speed is 6 metres per second, but its velocity, because it's travelling in the opposite direction, would be represented by -6 metres per second.

A 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 got those.

We can find a velocity of an object using the speed equation, but all we have to do is replace distance with displacement.

So if we do that, we end up with this equation.

Velocity is displacement divided by time, and if we represent that in standard symbols, it's V equals X divided by T.

So the displacement, X is measured in metres, the velocity, V in metres per second, and the time, T is measured in seconds.

We always need to remember to put the direction of movement in this as well, though.

Let's see if you can use that equation to calculate velocities.

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

So a car's travelling 500 metres north in 25 seconds.

Calculate the velocity of the car.

I write out the equation, V equals X divided by T.

I substitute in the two values.

So V equals 500 metres divided by 25 seconds and I've calculate velocity there 20 metres per second, but that's just the speed.

I also need to put the direction there for it to be a velocity, so the direction is north.

Now it's your turn.

I'd like you to try and find the velocity of this bicycle, please.

It travelled 60 metres to the left in 8 seconds.

So pause the video, calculate the velocity, and then restart.

Welcome back.

Your calculation should be like this, V equals X divided by T, put in the values and that gives a velocity of 7.

5 metres per second, and again, you mustn't forget to put left in there.

Well done if you got that.

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

An eagle flies north-east 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 north-east.

Well done if you 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.

So list any examples you saw in this lesson or other lessons and then you can 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 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 when adding them together.

The examples, velocity, displacement that we 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 part lesson in which we're looking at finding average velocities of things that are moving.

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 curved path there.

The second person, slightly shorter path.

Third person's zig-zaggy, and the 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 taken to reach point B is gonna be different for each of those four people, so their 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 than 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.

We've got Lucas travelling in a straight line from X to Y in 16 seconds and Andeep's travelling along the red path and 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 marked on the diagram.

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

Okay, welcome back.

And if we fill in the table we get these results.

You can see Lucas has the same average speed and average velocity because he went in a straight line.

While Andeep has an average speed of 0.

6 metres per second, but the average velocity is less because he's walked a further distance to end up at the same displacement.

Well done if you've got those.

Even when you're moving along a straight line, average speed and average velocity are not necessarily the same.

We can see an example of that using a number line here.

So we're gonna start off with displacement zero and we're gonna move forwards and backwards during this journey.

And we're gonna calculate average speed and average velocity at each stage.

So for the first movement, we move forwards 2 metres in 4 seconds.

We get an average speed of 0.

5 metres per second using the speed equation and using the velocity version of the equation, we get exactly the same answer.

Moving forwards again, 5 metres in 3 seconds, we calculate the average speed using that total time and the total distance travelled, 1 metre per second, and the average velocity, well, in this case, again, we use the total displacement and the total time and it's the same, because we've be moving in the same direction each time.

But now if we move backwards 2 metres in 3 seconds, we do the average speed calculation and in that we get 0.

9 metres per second.

But the average velocity is different and it's different because the displacement, the final displacement, and the distance travelled aren't the same, even though the time is 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.

Okay, welcome back.

Hopefully you selected B and D.

Her average speed is 0.

8 metres per second and her average velocity is 0.

6 metres per second forwards, being very careful there to specify a direction because it's a velocity.

The mathematics you needed to do is shown here.

And as you can see, you get different values because the distance and the displacement are different.

Well done if you got that.

Okay, it's time for the final task of the lesson now, and it's about a train travelling along a straight track, stopping at stations at a time shown in the table.

And as you can see, it starts at station A, moves to B, then to C, but then goes back to station B again.

What I'd like you to do is to calculate the average speed of the train between stations A and B, calculate the average speed of the train between B and C, calculate the average velocity of the train for the whole journey, and the average speed of the train for the whole journey as well, please.

So pause the video, work out the answers to those and restart.

Welcome back.

Here's the solutions to the first of those two questions.

The average speed between station A and B is 8.

0 metres per second, and the average speed between B and C is 10.

0 metres per second.

Well done if you got those.

And here are the answers to the second part, and here are the answers to Part 3 and 4.

The average velocity is plus 2.

0 metres per second, we used the displacement in that calculation.

And the average speed, we need to use the total distance travelled and that gives us an average speed of 7.

0 metres per second.

Well done if you've got those two.

Well, we've reached the end of the lesson now and here's a summary of everything we've covered.

Displacement is a vector that represents the distance away from a point and the direction, so how far away and what direction.

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

And for motion along a straight line, we use positive and negative values for this displacement and velocity, so we can describe the directions just by using plus and minus.

Average speed and average velocity are usually not equal to each other because there may be changes in direction of travel during any journey.

Well, that's the end of the lesson.

Well done for completing it.

See you in the next one.