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

This lesson's all about different speeds and in it, you're going to be revising how to calculate the speed of a wide range of objects.

You'll also be looking at what happens when objects are moving relative to each other, such as in opposite directions.

By the end of this lesson, you're going to be able to calculate the average speed of a wide range of moving objects.

You'll also know some typical speeds for human activities such as walking or running.

And finally, you're going to be able to calculate something called relative speed, which is a comparison of the speeds of objects which are moving together or moving apart.

This is a list of the keywords that'll help you understand the lesson.

The first of them is average speed, and you'll calculated average speed before at some point.

And lays at the speed of an object moving over a certain distance for a certain time.

Instantaneous speed is the second, and that is the speed at a very particular moment.

Magnitude is another word for size, the size of some sort of quantity.

And a scalar quantity is a quantity that only has size and we'll see quite a bit more about that later in the lesson.

And finally, relative speed, which is the speed of a pair of objects moving towards each other or apart from each other.

So it compose their overall speeds.

And here's an explanation of those keywords that you can refer back to at any point during the lesson.

This lesson's in three parts, and in the first part we're going to be revising how to calculate speed.

So we'll be looking at the speed equation and using that.

In the second part, we're gonna look at something called scalar quantities, and there're things that only have size, not a sense of direction, and speed's one of those quantities.

And in the final part we'll look at relative speed where we compare the movement of objects that are travelling in opposite directions or in the same direction and find out how fast they're separating or approaching each other.

So when you're ready, let's begin with the first part, which is speed calculations.

Okay, hopefully, you've seen this equation before.

It's the equation that links together distance travel, speed and time.

And it's simply, distance travelled = speed x time.

Now we often use symbols to represent the values in equations, and the symbols we've chosen to use are x for distance travel, so x is a distance.

V for speed and t for time.

So distance travelled, x is measured in metres.

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

Okay, let's quickly check if you can remember the symbols used the quantities and the units for motion.

So I've got a table here.

All I'd like you to do is to draw a series of lines connecting the symbol, quantities, and units together.

So draw a total of six lines please.

So pause the video, draw your lines, and then restart.

Okay, welcome back.

Let's have a look at the answers to that.

Well, first of all, speed has got the symbol v and it's measured in metres per second.

So you drew your lines at that.

Distance got symbol x and a unit metres, and that just leaves time with the symbol t and the unit s.

Well done if you've got all those.

Okay, we normally measure speed in metres per second, but there are other units we can measure it as well.

So what I'd like you to do is to decide which ones of these are alternative units for speed? Is it A, kilometres per second, B, miles per hour, C, millimetres per year, or D centimetres per day? And it can be more than one of those.

So pause the video, select all the ones that can be used to measure speed and then restart please.

Okay, the answers you should have chose there, all of them, all of those are units that we could use to measure speed because all of them are a distance divided by a time.

And we can use any distance divided by any time to get a unit for speed.

Well done if you spotted that.

Okay, we're gonna go through some examples of using the equation now.

So I'm gonna go through one and then I'd like you to try one yourself.

So I've got a speedboat travelling at speed of six metres per second.

How far will it travel in 25 seconds? So the way to answer these sorts of questions is like this.

First of all, you should always write down the equation 'cause that helps you learn and remember it.

So distance travel, equal speed x time.

The next thing I do is I try and spot the values for speed and time in the question, and I can see that the speed is six metres per second and the time is 25 seconds.

So a substitute those two values into the equation like this.

And finally, I just do the mathematics.

I multiply those together and that gives me a value of 150 metres.

Now it's time for you to have a go.

So I've got a jet travelling at a speed of 35 metres per second.

How far will that travel in 12 seconds? So pause the video, follow the same procedure as I did, and come to an answer, and then restart.

Okay, you should have written out the equation.

Distance travelled speed x time, substituted the two values from the question, 35 metres per second and 12 seconds and then performed the calculation by multiplying, that gives 420 metres.

Well done if you've got that.

So we've seen that you can calculate the distance travelled using that equation, but some of the times we want to work out how long it takes an object to move a certain distance at a certain speed.

So we can manipulate the original equation to find that.

So here's the original equation, distance travelled = speed x time.

And if we swap the sides of that to make it clearer, we get speed x time = distance travelled.

So all I've done is flip the sides of the equation, then I divide both sides of that equation by speed and it leaves me with a final version, the time is the distance divided by the speed.

And that's the equation I can use to work out time.

So let's have a little bit of a practise with that.

How much time will it take a scooter travelling at 5.

5 metres per second to travel a distance of 110 metres? So all I need to do is to write out the equation we've just seen.

Time is distance divided by speed, look careful at the question to spot those values, distance of 110 metres, speed is 5.

5 metres per second.

So write those two in and just do the calculation and it gives me a time of 20 seconds.

Now it's your turn, and what I'd like you to do is to answer this one.

A bicycle is travelling at 3.

0 metres per second.

How long will it take to travel a distance of 180 metres? Follow the same procedure as I did, and you should come to the answer.

So pause the video, get that answer, and restart.

Okay, what you should have done is this, write out the equation, spot those values in the question, 180 metres and 3.

0 metres per second, and then carry out the calculation giving an answer of 60 seconds.

Well done if you've got that.

The final version of the equation we're gonna see is the one that we use most often, and that is the version we use to find the speed from the distance and the time.

So we manipulate the equation in a similar way as before, we get the original equation, distance travelled = speed x time, we swap the sides over and then this time we divide both sides by time and that gives us a final version of the equation, speed = distance divided by time.

And as I said, that's probably the equation we're gonna use the most.

So let's have a go at using the final version of that equation.

I've got a question here.

Calculate the average walking speed of a person if they travel 1,110 metres in 750 seconds.

So as before, I write out the equation, this time its speed = distance divided by time.

I spot the distance and the time of the question and substitute those in, and finally, do the calculation, which give me 1.

48 metres per second, but we've rounded that to 1.

5 metres per second, as I've only got two significant figures.

It's time for you to have a go using the equation.

Here's your question.

Somebody runs 120 metres and 41 seconds, calculate their average running speed.

So pause the video, work out the answer to that and restart.

And here's the answer.

You should have written out speed = distance divided by time, substitute the values in, and that gives an answer of 2.

9 metres per second.

Well done if you got that.

We've just calculated a walking speed and a running speed.

And you do need to know some typical walking and running speeds.

So I'm gonna show you some of those now.

First of all, a typical walking speed is about 1.

5 metres per second.

Some people will walk a lot faster than that and some people will walk slower.

A typical running speed is about three metres per second.

Again, just typical value.

And finally, typical cycling speed is about six metres per second.

So obviously, it's the fastest of those three ways of moving, but they're just typical speeds.

If you wanna know record speed, I've got a table here, you can walk up to seven metres per second if you're an Olympic walker.

Obviously, the fastest sprinters can sprint up to 10 metres per second, perhaps a bit more.

And cycling, you can actually go about 80 metres per second at top speed.

So let's see if you can remember those typical speeds.

What I'd like you to do is to just draw lines matching the activities for the speed please.

So pause the video, draw those lines, and then restart.

Okay, welcome back.

Hopefully you remembered that running is about three metres per second.

Swimming wasn't on my earlier list, but you should realise you're going to swim slower than you can run, so that's 0.

5 metres per second.

Walking, 1.

5 metres per second and then cycling at six metres per second.

Well done if you've got those.

The speed equation that was used so far gives us an average speed between two points.

So if I've got a runner and they've run 50 metres in five seconds, I can work out their average speed, it's 10 metres per second.

But that doesn't give us the complete picture of the journey because that's just the average speed.

There's also something called the instantaneous speed.

And the instantaneous speed is how fast you are running at a very particular instant, a particular moment in time.

So near the start line on a sprinter starting off, the instantaneous speed won't be the highest value.

It'll just be something lower like three metres per second.

But as they've sped up during the journey, they're gonna have a higher instantaneous speed near the end, perhaps up to 12 metres per second.

So the speed is constantly changing as they're racing.

Let's see if you understand instantaneous speed here.

I've got a stone being dropped from the top of a high building and it's falling downwards following the path shown by those dotted lines there.

At which point will it have the greatest instantaneous speed? Will it be point A near the top, point B, bit lower, point C, a bit lower or point D, right near the ground? So pause the video, make your selection, and restart.

Okay, hopefully you chose point D because the stone's gonna be getting faster as it falls, it's gonna be speeding up because the force of gravity acts on it.

So it's highest instantaneous speed is going to be just before it hits the ground.

Well done if you've got that.

Okay, it's time for the first task now, and I'd like you to use your knowledge of speed calculations to answer this, please.

So the speed of sound in air can be estimated by observing lightning and listening for the thunder.

You may well have done this yourself.

A lightning flash is seen to hit a tower 2.

0 kilometres away and the sound of the thunder reaches the observer 6.

0 seconds later.

What I'd like you to do is to find what is the speed of sound in air, and then tell me what assumption you've had to make during that calculation.

So pause the video, answer those two questions and restart please.

Okay, welcome back.

The speed of sound in air can be calculated like this.

Two kilometres is 2,000 metres, so we needed to convert that distance to metres.

The speed is the distance divided by the time, so the distance was 2000 metres times 6 seconds, and that gives a speed of 330 metres per second.

And that's about the typical speed of sound in air.

The assumption you had to make to do the calculation was that the flash of light that came from that lightning strike reached you almost instantly.

And that's true, the time it takes the light to travel two kilometres is a tiny, tiny, tiny fraction of a second.

Well done if you've got those two.

Okay, it's time to look at the second part of the lesson now, and this is all about scalar quantities In physics, we have some quantities that only have size.

They don't have a sense of direction associated with them.

They can be large or small in size, but they they're not moving in a particular direction or pointing in a particular direction.

We call those quantities, scalar quantities.

Probably the easiest example is mass.

Mass is a scalar quantity, and we measure it in kilogrammes and we can have different amounts of mass, but it doesn't have any sense of direction associated with it.

So we can have a small mass and we can have a large mass, but we don't have a mass that's left or a mass that's right or up or down.

We just have different amounts of mass.

So mass is a scalar quantity.

Distance is a scalar quantity as well.

It's a measurement of how far you've travelled from a starting point, but it's not a measurement that's got a sense of direction associated with it.

So I've got a running track here, and if you run around the running track, complete lap, you travel 400 metres.

So you're around like this and this and back to the start.

So you've gone 400 metres, but you've finished where you started, but it doesn't matter if you've run in the opposite direction, you still run around the track and you travel a distance of 400 metres.

So the distance doesn't really depend on the direction you're running, it's just the overall number of metres you've covered as you travelled.

So distance is a scalar quantity.

Speed is also a scalar quantity in physics, it's a measurement of how much distance you cover every second.

So I've got a car here that's travelling at five metres per second, so it has a speed of five metres per second.

I've got a car here and is travelling in the opposite direction, but it's also got a speed of five metres per second.

So its speed is just represented as five metres per second as well.

The direction of the speed doesn't matter.

So speed is scalar and both of those cars have the same speed, even though they're going in opposite directions.

Okay, let's see if you understood that.

I've got two swimmers and they take the same time to swim a length in a pool, but they're swimming in opposite directions.

They have the same average speed, is that true or false? And once you've made your decision on that, I'd also like you to justify your answer.

Is it A, they cover the same distance each second on average and their direction does not affect the speed? Or is it B, they cover the same distance each second on average, but their different directions means that their speeds are different.

So pause the video, make your true or false selection and your justification and then restart.

Okay, welcome back.

Well, that statement was true.

They do have the same average speed, and the reason for that is because the direction does not affect their speed.

They're covering the same distance each second, so the speed is the same.

Well done if you've got those two.

Now it's time for the second task of the lesson.

This is all about scalar quantities, but it does involve some speed calculation as well.

So in a race, a car completes 10 laps of a four kilometre oval track in 70 minutes.

The car finishes exactly where it started.

What I'd like you to do is to calculate the average speed of the car in metres per second please.

And then explain why that results shows that speed is a scalar quantity.

So pause the video, answer those two questions and restart.

Okay, welcome back.

Well, the calculation of average speed here is a bit more complicated than the other examples.

The first thing I needed to do was to find the time and there were 17 minutes and it's 60 seconds in each minute, so that gives me a time of 1,020 seconds.

Then I needed to calculate the speed and I need the distance for that.

And the overall distance is 10 laps of four kilometres, so that's 40 kilometres and that's 40,000 metres.

So I can write those values in here.

The speed then gets to a value of 39 metres per second, which is pretty fast even for a car.

Then we needed to explain why the result shows that speed is a scalar quantity.

Well, the speed was calculated from the distance travelled, not from how far away we were from the starting point.

If we'd have used that value, well, we finished in the same places as we started, so we'd have travelled a distance of zero metres giving a speed of zero, and it clearly wasn't that.

So the speed must be calculated from the distance travelled, not from how far away we are from the starting point.

Right now it's time for the final part lesson, this is all about relative speed, and we're gonna be looking at pairs of objects that are both moving.

All the examples we've looked at so far, when we're measuring speed, we're measuring speed compared to a fixed point.

So when we were looking at people racing, we measured speed compared to the start or the finish line.

In other examples, we could measure the speed of an object moving compared to a point on a map for a journey, or if it was a scientific experiment, we measure the speed compared to a fixed sensor or a line withdrawn on a track or something like that.

So we're measuring speed relative to fixed points most of the time.

But that's not the only way we can measure speed, sometimes we're comparing the speeds of two objects that are both moving.

So we're looking at the speeds in relation to each other.

We call that the relative speed.

So the object could be doing several different things.

They could be moving in the same direction.

So if you're in a race and you are overtaking somebody, you're moving in the same direction at a slightly higher speed than them, or they could be moving in opposite directions.

And you might have seen this happen when you're on trains, you go in one direction the train passes, all seem like very quickly in the opposite direction.

So we've got two different sorts of relative speed there.

The relative speed is the difference in the speeds taking to into account the direction of travel of the two objects.

And so relative speed depends upon the speeds of the two objects and the directions they're going in.

Are they going in the same direction or opposite directions? So if I've got two trains and they're passing each other at similar speeds to each other, they'll seem to have a low relative speed.

They'll take a long time for one train to overtake the other.

But if those two trains were travelling at the same sorts of speeds, but in opposite directions that seemed to travel past each of them very, very quickly, they've got a higher relative speed.

So I'd like you to look carefully at this diagram and tell me which of those situations will give the highest relative speed.

I don't need you to work out what that relative speed is.

I just need you to decide in which of those three scenarios A, B, or C will there be the greatest relative speed.

So pause the video and restart when you're ready.

Okay, welcome back.

Hopefully you chose C, that's got the highest relative speed because those objects are both moving and they're both moving in opposite directions to each other.

So they're gonna have a high relative speed and I'm gonna show you how to calculate that in a moment.

Okay, let's have a look at an example of how to find a relative speed of some objects.

I've got two runners, runner A is travelling at five metres per second, and then we've got runner B who's behind, and they're travelling at six metres per second.

So runner B is gonna be catching runner A.

So runner A is 10 metres ahead of runner B.

We can see that runner B is catching up to runner A 'cause they're going faster.

And they're gonna close that gap by the difference in the two speeds because they're running in the same direction.

So over time, every second runner B is gonna close that gap by one metre.

So they're closing the gap at one metre per second.

And we've found that by subtracting the smallest speed from the larger speed though.

So the relative speed of runner B to run A is a different to the speeds, that's one metres per second.

Let's see if you can find the highest relative.

I've got three pairs of runners here, and all I'd like you to do is look carefully at the values of their speeds and decide which of them has got the greatest relative speed or which pair, is it A, B, or C? So pause the video, make selection, and restart.

Okay, welcome back.

Well, hopefully you chose A and the relative speeds of each of those as shown here.

You can see it's a difference in those speeds.

So A has got a relative speed of two metres per second.

B, the gap in those speeds is only one metre per second.

And C, even though they're going in opposite direction, that doesn't matter, it's a difference in those speeds, it's 1.

5 metres per second.

So well done if you select A.

Now we've seen relative speed when two objects are moving in the same direction, we can also look at relative speed when objects are travelling in the opposite directions.

So we'll use some cars for that.

I've got a car here that's travelling at eight metres per second towards the right, and the second car here's travelling at seven metres per second towards the left.

And those two cars are 30 metres apart.

Now because they're travelling in opposite directions, they're going to close that gap at 15 metres per second.

One second on from where this picture is, that gap's gonna have shrunk down because the green car's gonna have moved eight metres towards the right, the red car, seven metres to left.

So that gap is shrunk by 15 metres.

So the gaps are closing that gap at 15 metres per second.

We've added the two speeds to get the relative speed because they're approaching each other.

So the relative speed of those cars is the sum of the speeds when they're approaching each other, and that's 15 metres per second.

As before, I'd like you to identify the greatest relative speed here.

So I've got pairs balls moving towards each other, which has got the greatest relative speeds of which set, is it A, B, or C? Pause the video and restart once you've made your selection.

Okay, welcome back.

Hopefully you selected A, that's got the greatest relative speed.

And if we work out those relative speeds, we see how quickly they're closing the gap.

That's six metres per second for A, we've added those two values together.

For B, it's only five metres per second, and for C 5.

2 metres per second.

So well done for selecting A.

So now let's work through an example.

I'll do one and then I'll ask you to try one.

So calculate the relative speed between two skaters travelling in opposite directions, one at 4.

5 metres per second, and the other at 5.

5 metres per second.

So because they're going in opposite directions, I can add the sum of those speeds.

So relative speed is the sum of those two speeds.

So add those two speeds together and that gives me a relative speed of 10 metres per second.

Now it's your turn.

I'd like you to calculate the relative speed of a car travelling at 9.

5 metres per second, which is overtaking a car travelling at 8.

2 metres per second.

So these cars are travelling in the same direction.

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

Welcome back.

These two cars are moving in the same direction.

So the relative speed is the difference in those speeds.

So we find the difference in those speeds like this, and that gives an answer of 1.

3 metres per second.

Well done if you've got that.

One of the reasons we need to understand relative speed is because it's important during collisions.

If things crash together, the direction that the objects are moving is very, very important.

So the higher the relative speed, the greater the damage caused during a collision.

So if I've got two cars moving in the same direction, they can collide without too much damage if they're going in exactly the same direction and the relative speed is not too high.

So this is the typical result of a car that has hit another car at a fairly high speed, but both cars were travelling in the same direction, so the collision didn't cause too much damage.

If I have cars that are travelling on a town road, they can travel up to 30 miles per hour, and that's about 13 metres per second.

So the maximum speed they can collide in head on is 26 metres per second.

And that results in damage, a little bit like this.

You can see there's quite a lot of damage to the front of the car, but at those relative speeds, the collision is usually survivable.

On a motorway, a car might be travelling at 70 miles an hour, and that's 30 metres per second.

So cars travelling in those opposite directions would've a relative speed of 60 metres per second.

And as you can imagine, a head-on collision with that sort of relative speed causes a huge amount of damage, and they're usually not survivable collisions.

Okay, let's see if you understand the importance of relative speed and collisions.

Why are barriers placed between opposite sides of a motorway, but not between lanes on a town road? And you can see the crash barriers there separating those two lanes on the motorway.

So is it because the average speeds of the cars on the opposite sides is very high? Is it because the relative speeds of the cars on the same side is very high? Or is it because the relative speed of the cars on opposite sides is very high? So pause the video, make your selection and restart.

Hello again, and hopefully you chose C.

The relative speeds on opposite sides are very high, so those cars moving in opposite directions on opposite sides, if they crash together, there'd be a huge amount of damage.

So these crash barriers in the middle are those to separate them.

Well done if you did that.

Okay, we're up to the final task of the lesson now.

So I'd like you to try this one.

There are two swimmers in a race.

Swimmer A is travelling at 1.

2 metres per second and is 30 metres from the finish line.

And swimmer B is travelling at 1.

5 metres per second and is six metres behind the swimmer A.

I'd like you to work out the relative speed of the swimmers, then I'd like you to work out how long it'll take for swimmer A to catch up with swimmer B? And finally, I'd like you to try and work out who would win the race if their speeds stay the same? So pause the video, try and work out the solutions to those three and restart, please.

Okay, welcome back.

Let's have a look at the answers to that.

Well, the relative speed of the swimmers is not 0.

3 metres per second.

They're going in the same direction, so all I need to do is find a difference in speeds.

Then to find out how long it'll take the swimmers to catch up, well, the distance between them was 6.

0 metres and the relative speed is 0.

3 metres per second.

So the gap is shrinking by 9.

0 metres every second.

So I can use this calculation and find it takes 20 seconds for swimmer B to catch up to swimmer A.

Well done if you've got those two.

The final part is a little bit more difficult.

Who will win the race? Well, what I can do is find out how long it takes A, swimmer A, to reach the finish line and it use a speed calculation, it's gonna take them 25 seconds.

So it took swimmer B 20 seconds to catch up and they're going faster so in the end, swimmer B is going to catch up and pass them after 20 seconds, so they're gonna win the race.

Well done if you've got that.

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

Speed is a scalar quantity, so it's got size, but it doesn't have direction.

It's just got magnitude without any sense of direction.

The speed equations are shown there: Distance travelled is speed x time, or x equals v times t.

Speed = distance divided by time or v equals x divided by t.

Time = distance divided by speed, or t equals x divided by v.

Now the relative speed is the difference in the speed taken into account the direction of travel.

So if the objects travel in the same direction, we need to subtract the speeds to get the relative speed.

And if the objects travel in opposite directions, we need to add the speeds to get the relative speed.

And I've shown that in the two little figures though.

So well done for reaching the end of the lesson.

Hopefully, I'll see you in the next one.