Lesson video

Hello there, I'm Mr. Forbes and welcome to this lesson from the Measuring and Calculating Motion Unit.

The lessons called Displacement of Velocity as Vectors.

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

We'll be seeing how to combine displacement 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 four key keywords that you need to understand to help you in this lesson.

The first is displacement and the displacement of something is the distance from its starting point and the direction.

The second is vector, and a vector quantity has a size or magnitude and a direction associated with it.

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

And the final one is centripetal force and centripetal forces are forces that cause objects to move in circles.

And here's the explanation of those keywords, again.

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

The lessons 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 there are 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 that those two distances are different.

One of them is a straight line distance and one of them is the shortest distance you can 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's 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 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 or so a vector quantity has direction and also magnitude or size.

And whenever you're specifying a vector, you need to specify the direction, otherwise you are 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 your understanding here, which of those measurements though are displacement 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 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.

I'll position Izzy 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 north-east 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 south-east.

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 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 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 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 north-east, north-west, south-east 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 maps on one side of it and negative displacement maps 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 dis 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 a 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 restart.

Okay, and the reason that 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 in 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 first type of movement they do is they walk forwards two metres.

So if the distance they've travelled is two metres and you can see from the diagram their displacement is plus two metres.

They two 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 three metres and their displacement is plus three metres.

But now I've given the instruction to walk backwards five metres.

So she's walked backwards five metres there.

Her distance travelled is increased by five metres, she took 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 at displacement zero and distance travel zero.

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

So my first instruction move right four metres, distance travel 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 from 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 and four metres south and five metres north again, what's the total distance travelled and her displacement from the starting position? So to find a 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 a 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 use west as positive, then you'll find a 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 into 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 though.

You might be travelling a hundred 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 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 a 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.

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 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.

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 a 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 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 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 travels 60 metres to the left in eight 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've 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'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.

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'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 when adding them together.

The examples, velocity, displacement that we're seeing in this lesson, momentum, force and acceleration, you'll see else were.

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 going to 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 is zig-zagy and the final person, they loop round 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.

The 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 loss is 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 Andeeps travelling along the red path.

It takes 20 seconds.

I'd like you to calculate their average speed 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.

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 a average speed of 0.

6 metres per second, but the average velocity is less because is got 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 two metres in four seconds.

We get an average speed of 9.

5 metres per second.

Using the speed equation and using the velocity version of the equation, we hit exactly the same answer.

Moving forwards again five metres in three seconds.

We calculate the average speed using that total time and the total distance travelled, one metre per second.

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 been moving in the same direction each time.

But now if we move backwards two metres in three seconds, we do the average speed calculation and in that we get 9.

9 metres per second.

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

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

I've got another description of Sophie walking and 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 forward.

Being very careful though 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.

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 round 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, it's 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 the 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.

For any object that's moving in a circle, even at constant speed is going to be a changing instantaneous velocity.

So I've drawn an object here, it speeds the same, but the velocity is constantly changing.

Now because the velocity is changing, there must be a force acting on the object and that force is causing that acceleration.

That force is also always acting towards the centre of the circle to change the direction of motion.

So we've got a force acting towards the centre of a circle causing circular motion and we call those type of forces centripetal force.

Forces directed at the centre of a circle.

You can quite easily demonstrate centripetal forces by swinging a piece of cork around above your head.

So if you attach something fairly light at the end of a piece of string and spin it above your head in a circle.

So there's your head there, there's a string and there's the circular path.

If you spin that around, then the cork will follow circular motion.

It'll travel in a circle and it travels in that circle because the string is always pulling the cork towards you as you spin it above your head.

So the force is always acting towards the centre, a centripetal force.

Let's check if you understand about the direction of forces here.

Which of those diagrams shows the forces acting on an object travelling the circle? So pause the video, make your selection, and restart.

Welcome back, you should have chosen C.

The forces are always directed at the centre of the circle.

It's a centripetal force.

Well done if you chose that one.

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 movements changed.

Well done if you got that.

And here are the solutions to the other three questions.

The average speed of the car was 12 metres per second.

The average velocity of the car was 11 metres per second.

And I've drawn a red arrow on the diagram there to show the direction of the average velocity.

Well done if you've got those.

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

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

So how far and in what direction? Velocity is a vector that represents the speed in a particular direction.

So speed and direction need to be specified.

If you are just looking at motion along a straight line, we can use positive and negative values instead of having to explain the directions.

The instantaneous velocity of any object travelling in a circle is always changing, even if the speed of the object isn't.

And that's because the direction changes.

And for that change in velocity, you need to have a centripetal force acting towards the centre of the circle to make the object move in the circle.

Well done for reaching the end of the lesson.

I'll see you in the next one.