Hello there, I'm Mr. Forbes, and I'll be leading you through this first lesson in the Moving by Force unit, which is all about calculating speed.

By the end of this lesson, you'll be able to calculate the speed of a wide variety of different objects based upon the distance they travel and the time it takes to travel that distance.

You'll also be able to do a range of other calculations such as calculating how far an object's moved in a different amount of time, or how long it'll take an object to travel a certain distance.

You might need a calculator during this lesson, so if you have one, get it out now.

And when you're ready, we'll begin.

In this lesson, you'll meet a variety of words you need to understand to fully get the best of the lesson.

That includes distance, time, speed, metres per second, or m/s, and miles per hour, mph.

These are the definitions of those keywords and examples of their use.

If you get confused at any point in the lesson, you can return to here and check them out again.

The lesson has three parts.

In the first part, we're just going to try and describe faster and slower moving objects, and get a clear picture of what we mean by speed.

In the second part, we'll do some calculations of speed using a speed equation.

And in the final part, we'll go a bit more advanced, and we'll start to use some different units of speed such as miles per hour.

So let's get straight on with the first part, faster and slower.

So you've probably got a reasonable understanding of what speed is, but let's just double check that and go through a few examples.

Speed is a measure of how fast an object's going.

We have fast objects which have high speeds and we have slow objects which have low speeds.

And it's basically a measure of how fast the object is travelling from one place to another.

Here's a couple of examples of things travelling at different speeds.

Let's have a look at an object that travels at a very slow speed, a very small distance every second.

An example's a snail.

A snail will travel at something like a millimetre per second at its top speed.

Obviously, we wanna compare that with something that travels quite quickly.

So we've got an object that's travelling a large distance every second that's got a high speed.

And that example is a jet plane.

This one is Concorde, which travels three times faster than sound at its peak.

But unfortunately it doesn't fly anymore.

It's retired.

So a speed of 600 metres every second is a common speed for Concorde to fly up.

So let's check if you understood what I meant by speed there.

I'd like you to say whether this is true or false and then justify your answer.

A car travelling faster is a greater speed than a car travelling slow, and is that because the faster car covers a greater distance each second, or the faster car travels for a shorter time? I'd like you to pause the video and select answers to those two, and then restart when you're happy.

Welcome back.

You should have selected the answer true.

A car travelling fast has a greater speed than a car travelling slow.

And the reason for that was that the faster car covers a greater distance each second.

It's going at greater distance every second.

So well done when you selected those two.

Right, we're gonna compare some cars.

And we've got two cars that are gonna be travelling for one second, and we're gonna see the difference between those two cars and what it means by having a different speed.

So I've got our green car, which is faster at the start.

And I've got a red car, which is a bit slower at the start.

And we're gonna allow them both to travel for one second.

So here they go.

There's the green car travelling for one second.

And there's the red car travelling for one second.

And you should see the results.

It's fairly obvious the green car has travelled a greater distance than the red car.

The green car is faster, and it's gone a greater distance after one second than the red car, which was slower.

15 metres for the green car and 10 metres for the red car.

So our conclusion from that is the faster cars travel greater distances in the same amount of time.

I've got a second check for you here to see whether you understood that.

This time, I've got objects travelling for two seconds instead of one second, but it's the same principle.

Two toy cars have a race.

A red car travels at 4 metres in 2 seconds and a green car travels 6 metres in 2 seconds.

Which of those cars is travelling at high speed? I'd like you to just pause, and select the answer, and then restart.

Great.

So the answer to that was the green car.

The green car has covered 6 metres in 2 seconds and the red car only 4 metres.

So the green car must have been travelling at a higher speed 'cause it's gone a greater distance in the same amount of time.

So, well done if you've got that.

Here's our next example.

I've got two cars at different speeds, but this time they're travelling a fixed distance, not for a fixed time.

So again, I've got the green car and I've got the red car.

The green car's faster than the red car.

And we're going to see what happens when they travel 15 metres.

Here we go, a length of 15 metres there.

And the two cars are travelling.

And what you should see from that is the green car has covered that 15 metres in a shorter time.

The time it took to travel 15 metres is less than for the red car.

So the faster car took only 2 seconds.

The slower car took 3 seconds to cover that distance.

And what we can say about that is the faster car travels the same distance in a shorter period of time.

So let's check your understanding about what the different cars do.

We've got two toy cars having a race along a 3 metre long track.

So they're both travelling at the same distance this time.

The yellow car took 4 seconds to each the end of the track, and the blue car took 6 seconds to each the end of the track.

Which of those cars was travelling at higher speed? Pause the video and select your answer, and then restart and we'll check it.

Great.

The answer was the yellow car.

The yellow car has taken a shorter period of time to travel the same distance than the blue car.

So, well done if you've got that question right.

Right, we're here at the first checkpoint to see if you've understood what's going on, our first task.

So I've got two separate questions here for you to have a look at, and I want you to compare the speed to some objects and rank them.

Okay, so in the first one I've got Table 1.

It shows the time it took five different swimmers to complete a race.

We've got five swimmers, A, B, C, D, and E.

And we've got their times underneath them.

A, 25 seconds, B, 26, C, 31, D, 27, and E, 28 seconds.

And I want you to rank those in order of which is the fastest or slower, writing first as the fastest and fifth as the slowest.

Okay, and then for question two, a similar sort of activity, but this time, they're all travelling for the same amount of time but they're going different distances.

So at Table 2 showing the distance some joggers run for 50 minutes.

I want you to rank the joggers in order of their speed as well from first fastest to fifth the slowest.

So pause the video and try and answer that, and I'll go through the answers.

Great.

And here's the answers.

And hopefully you got these right.

We'll have a look and then go through them very briefly.

We've got swimmer A, and they only took 25 seconds to cover this, and so that's the shortest period of time, so they were first.

Swimmer B took 26 seconds, that's the second shortest time, so they're the second fastest.

And so on, all the way down to swimmer C.

They took 31 seconds, that's the longest amount of time, so they must have been the slowest swimmer to cover that distance.

They're the fifth.

And to question two, again, what we're looking for, the fastest person would've covered the greatest distance in those 50 minutes.

And that was runner J.

Runner J has got 4.

2 kilometres they've run.

That's the greatest distance of them all.

And the slowest there is Runner H.

They only covered 1.

8 kilometres, which is, to be honest, further than I could have run.

Okay, we're on to the second part of the lesson, and we're gonna look at speed calculations.

And it's here where you're probably gonna need your calculator because we're gonna be doing quite a bit of mathematics and using a fairly straightforward equation.

But you are allowed to use a calculator, so why not? All right, when we're talking about speed in physics, we nearly always talk about speed in metres per second.

How many metres an object will travel in each second? And we often use the word per instead of each.

I'm gonna use both and try and get you used to both.

But per in physics just means each.

So 50 metres per second is 50 metres each second.

A car travelling 5 metres each second would be given a speed of 5 metres per second when we use that sort of language.

Metres per second is written as m/s, 'cause we don't want to have to write out the words every time.

So we use quite a lot symbols.

So the speed of the car in that previous example was 5 m/s.

I would say that out loud as 5 metres per second.

Okay, a quick check of that.

Which of these is the correct way of showing the speed in metres per second? Is it A, 8 meters/sec? B, 8 m/sec? C, 8 meters/s? Or D, 8 m/s? And I'd like you to pause the video, make your selection, and then restart.

Welcome back.

The answer to that was 8 m/s.

Metres is written as m, seconds written as s, and the slash means per.

Okay, so 8 m/s is eight metres per second.

And that's the correct way of writing out speeds in physics.

Okay, next we're gonna look at where we get an equation that links speed, distance, and time together.

We're gonna get a mathematical expression.

We're gonna use it to calculate as distance an object moves 'cause that's the easiest approach to take, right? The rules that we come up with will describe a mathematical relationship between distance, speed, and time.

Something we call an equation.

Starting from the idea that speed is the distance travelled every second, we can get that expression for speed related to distance and time.

Imagine a cyclist travelling at a speed of 3 metres a second.

How far, or what distance, will they travel in 6 seconds? Well, they're going 3 metres every second.

That's what 3 metres per second means.

So what we're gonna do is add up each of those 6 seconds.

In the first second, they travel 3 metres, so that's second 1, 3 metres.

In the second second, another 3 metres.

And the third second, another 3 metres.

And so on, fourth second, fifth second, and sixth second.

And to find out how far they've travelled, all we need to do is add up those 6 separate seconds, those 6 separate distances we got there.

So adding all those together will give us a speed, sorry, a distance of 18 metres.

So in 6 seconds, they travelled 18 metres.

Looking at the relationship, and it's 3 metres every second for 6 seconds, or times 6 seconds is 18 metres.

And that's our speed equation.

The speed times the time will give us the distance they travelled.

Here's a second example of that, just to make sure that we understand it properly.

We've got a faster cyclist travelling at 3 and a half metres per second, 3.

5 metres per second.

What distance do they travel in 6 seconds? Well, it's 3.

5 metres every second for 6 seconds.

So in the first second, 3.

5 metres is how far they travel.

The second second, another 3.

5.

Third second, fourth second, fifth second, and finally, the sixth second.

If we add all those together, again, we can find the distance they travelled in those 6 seconds.

And doing a bit of maths, that's 21 metres.

So this cyclist has travelled 21 metres in 6 seconds.

They're going 3.

5 metres every second for 6 seconds.

It gives 21 metres.

And again, that gives us an expression linking those factors together.

The speed times the time gave us the distance travelled.

So, to check if you've understood exactly that process I just carried out, let's have a look at another example for you to do.

I've got a boat travelling at a speed of 5 metres per second.

What distance does it travel in 4 metres? I'd like you to use the same procedure I did and come up with an answer for me.

So pause the video, and once you've selected an answer, restart it and we'll check.

Welcome back.

Your answer should have been 20 metres.

The process you used would be something like this.

We've got 5 metres every second for 4 seconds.

That's 5 metres plus 5, plus 5, plus 5, for those 4 seconds in total, giving a total distance of 20 metres.

So, 5 metres every second for 4 seconds is 20 metres.

Well done if you came up with that solution.

All right, putting together all that information, we come up with what's called the speed equation.

This is the equation that links distance, travel, speed, and time for any object that's moving.

And it's written as this, distance travelled equals speed times time.

And you should see that was true for all the examples we've done so far.

So we are going to have a look at using that equation for some simple examples.

Now, I'll lead you through one, and then I'll ask you to do one yourself.

So we've got a motorcycle travelling at a speed of 6 metres per second.

How far will it travel in 15 seconds? And the process I always like to do is write down the equation.

Writing down the equation helps me to remember it, and also makes getting to the answer much easier 'cause I'll just put values into that equation.

So there it is, distance travelled equals speed times time.

And then, I looked at the question, and I try and find the speed and the time and put them into the calculation instead of the words.

So, looking carefully at the question, the speed was 6.

0 metres per second, so I put in 6.

0 instead of speed.

And how far did it travel in 15 seconds? That gives me the time of 15 seconds, so I put that in for time, 15 there.

And then it's just a simple matter of multiplying those two together and that'll give me the distance travelled.

Distance travelled is 90 metres.

6.

0 times 15.

Okay, this is an example for you to solve.

I'd like you to follow the same process exactly as I did.

So pause the video, and once you've got a solution, restart.

Welcome back.

The process you should have followed is exactly the same as mine.

Write down the equation, look at the question and try and find the speed.

That's 3.

5.

Look again, and try and find the time.

That's 22.

Put those two values into the equation like this, and then finally, just multiply those two together to come up with an answer.

77 metres is the answer to that one.

Well done if you got that.

Okay, we saw earlier that the greater the speed of an object, the less time it would take to travel a certain distance.

So for example, if we've got a sprinter, they're running at 10 metres per second.

They'll take less time to finish 100 metre race than somebody running at 8 metres per second.

Similarly, if you've got a horse that's galloping at 15 metres per second, it's gonna finish your race in less time than a horse galloping at 13 metres per second.

The time taken for those athletes or horses to complete the race can be calculated from that speed equation that we saw earlier.

I'm gonna show you an example of calculating the time it takes to complete a certain distance when travelling at certain speed.

So the example I've chosen is here.

How much time will it take for a car travelling at 30 metres per second to travel a distance of 96 metres? And to solve that, I use the same approach as before.

I write down the equation.

Distance travelled equals speed times time.

And this time, I substitute in the distance travelled, and I substitute in the speed of the objects.

So I put those values in instead, because I don't know the time yet.

So I write it out like this.

I've substituted the distance travelled, 96 metres.

And I've substituted in the speed, 30 metres per second.

And I get an expression like that.

Now, I can rearrange that expression by dividing both sides by 30, and that will give me an expression like this.

96 divided by 30 is equal to the time.

And finally, I can solve that by actually dividing 96 by 30 and that will give me the time it took.

And that is 3.

2 seconds.

So, it took 3.

2 seconds for that car to cover 96 metres.

I've got a second example here for you.

And I'd like you to follow the same procedure exactly as I did to be able to find the time for this.

A toy is travelling at 2.

5 metres per second.

How much time will it take to travel a distance of 16 metres? Pause the video and use the same processes I used there, and you should be able to come up with a solution for the time.

So restart once you've done that.

Okay, welcome back.

Let's have a look at the process.

You should have done the same as me before.

Right now, the equation, distance travelled equals speed times time.

Put the numbers in from the question.

Distance travelled was 16, speed was 2.

5 times a time.

We shift the equation around so that we get time on its own on one side of it, just like this.

16 divided by 2.

5 equals the time.

And finally, calculate the time by doing that sum on our calculators, and that should give you an answer of 6.

4 seconds.

Well done if you did that.

So far, we've calculated the distance travelled by movement object and the time it takes to get there.

But we haven't calculated speed yet.

So what I'm gonna do is rearrange this equation so it's in terms of speed, 'cause speed is the thing we wanna calculate most often.

First thing I do is I swap the sides of the equation like this.

And then all I have to do is divide both sides by time, and I get an equation like this, which allows us to calculate the speed quite easily.

So let's look at an example of using the equation in that form.

Here's a question.

Calculate the speed of a car when it travels 450 metres in 25 seconds.

I write down the equation, this time using the speed equals distance divided by time version of it.

I substitute in the two values, and then I just use my calculator to find the answer to that, 18 metres per second.

So I'm gonna ask you to have a go at answering this version of the question.

And use the same equation as I just did.

So pause the video, follow the same steps as I did, and then restart the video when you've got an answer.

Okay, here's what you should have done.

Write down the equation, substitute in the values, and get an answer using a calculator.

8 metres per second.

So, well done if you've got that.

Okay, it's time for your task.

The task here is to complete this table.

You're gonna be using the equation in the three different ways I've shown you to calculate distance, time, and speed for different objects.

I've got a range here, camera drone, athlete, skateboard, sailing boat and aeroplane.

And I've got data about the distances, times, and speed.

But in each row of the table, there's one value missing.

I'd like you to find that missing value, complete the table.

So pause the video, use the equation to solve all five of those, and then restart, and we'll see what your solutions were.

Okay, let's have a look at the answers to those.

You should have completed the table with these answers.

I've got a camera drone that has travelled a distance of 80 metres.

The athlete took 50 seconds.

The skateboard, 15 seconds.

The sailing boat was travelling at a speed of 85 metres per second.

It seems a bit high for me.

And the aeroplane travelled at 240 metres per second.

Okay, we're moving on to the final part of the lesson, and this is about using other units for speed.

We've used metres per second for all of our calculations so far, but there are quite a few different variations of how we can measure speed.

You have heard of some of them already such as kilometres an hour, or miles per hour.

But there are a wide variety.

So as I said earlier, metres per second is not the only unit we use for speed.

We can use any distance and any time measurement to actually do it.

As long as we use a distance divided by a time, we end up with a unit for speed.

So here's three examples.

I've got a toy train set.

That train isn't going to move many metres per second, it's gonna be moving some centimetres per second.

So it might be more convenient to measure its speed in centimetres per second.

I've got a motorcycle travelling there, and it's gonna be travelling many metres every second.

So I might want to actually measure in a unit based upon the largest timescale.

So for the motorcycle, I might measure how many kilometres, how many thousand metres it goes every hour.

So kilometres per hour is a very common unit for speed.

And similarly in the UK, we often use miles per hour for an object that's moving.

Many other countries don't use miles, but we still do.

Okay, quick check of your understanding about units of speed.

Which of these can be used to measure speed? And there's three correct answers here.

So I'd like you to pause the video, select the three correct answers, and then restart.

I'll come back looking at the examples here.

Kilometres per second can be used for speed.

Millimetres per second could be used for speed.

And centimetres per hour could be used for speed.

Because all of those are a distance divided by a time.

The only example that's wrong is centimetres per metre.

That wouldn't give you a unit for speed at all.

That's not the correct answer.

I'm gonna show you an example now of how to use those different units in a speed calculation.

So here's a question.

A car travels a distance of 92 kilometres in a time of 4 hours, calculate its speed.

I'm gonna follow the same processes I've been following throughout the whole lesson.

First thing I'm gonna do is write down the values from the question.

Distance is 92 kilometres.

The time is 4 hours.

Next thing I do is write down the speed equation.

Speed equals distance divided by time.

And substitute those values in, the distance 92, and the time of 4.

And that gives me an answer of 23.

Well, here's where I've gotta be careful.

And it's not metres per second anymore.

I'm using kilometres and I'm using hours.

So the unit I need to put here is based on kilometres and hours.

It's kilometres per hour.

Kilometres per hour just like that.

Another example now, a car travels 320 miles along a motorway in 5 hours, calculate the speed of the car.

Just as before, write down the equation, substitute in these two values, and that'll give you an answer of 64 miles per hour.

So here's a question for you to answer.

I'd like you to follow exactly the same processes.

So pause the video, calculate the answer, and then restart the video when you're happy.

Okay, so here's what you should have done.

Written down the the equation, speed equals distance divided by time.

Substituted in those two values, write them there.

And if you look carefully, it's centimetres and seconds.

So your speed answer should be 5.

0 centimetres per second.

There's another way you can answer these sorts of questions, and that's to convert the units that you've given into those standard units of metres per second.

So let's have an example of that.

A toy train travels at 440 centimetres in a time of 20 seconds, calculate the speed.

So just as before, I write down the distance and write down the time, but I convert them to the standard units this time.

So 440 centimetres, that's 4.

4 metres.

So, writing down the equation, speed equals distance divided by time.

Speed is 4.

4 divided by 20.

And that gives me an answer of 0.

22 metres per second.

And it's metres per second because I've converted the units to metres.

Okay, a quick check for you here.

I'd like you to calculate the speed of a cyclist in kilometres per hour if they travel 7.

5 kilometres in 15 minutes.

Pause the video and work out your answer, and then restart.

Okay, welcome back.

And let's see, the answer should have been 30 kilometres per hour.

And to get that, you needed to know 15 minutes is not 0.

25 hours, it's a quarter of an hour.

Write down the equation, substitute those two values in, and that give us the answer 30 kilometres an hour.

Well done if you've got that.

Okay, we're at the final task now, Task C.

And what I'd like you to do is use that new knowledge to calculate some more speeds.

I'd like you to calculate speed of the following two objects in the units that are given in the question.

A snooker ball travelling 140 centimetres in 2.

5 seconds.

A jet travelling 540 kilometres in 45 minutes.

And of question two, a car travels a distance of 80 kilometres at a time of 2 hours.

I'd like its speed in kilometres per hour and its speed in metres per second, please.

So pause the video, work through those, and then we'll go through the answers together in a minute.

So, welcome back.

Let's go through each of those.

The first one's snooker ball travelling 140 centimetres in 2.

5 seconds.

Speed is distance divided by time.

Put in the two values.

Naturally giving you a speed of 56 centimetres per second.

For the second one, a jet 540 kilometres in 45 minutes.

Speed equals distance divided by time.

Put in the distance and the time, which I'm gonna leave in minutes, that's giving me a speed of 12 kilometres per minute.

The next part now, we're gonna calculate speed and kilometres per hour.

So that's speed equals distance divided by time.

80 divided by 2.

40 kilometres per hour.

But now we need the speed in metres per second.

We've gotta do some conversion here.

So the distance travelled is 80,000 metres, that's 80 kilometres.

And the time, 2 hours, 7,200 seconds.

So again, use the equation, put the values in, and that should give you a final answer of 11 metres per second.

Well done if you got that.

That was a fairly tricky one.

Okay, we're at the end of the lesson now.

A quick summary of what you should have learned.

You should have learned, the greater the speed of your object, the less time it takes to travel a certain distance, the greater the distance it travels in a certain time.

You should also know speed's measured in metres per second, but it can be measured in a quite a wide range of other units.

And we've seen two versions of the speed equation.

One that gives us distance travelled, which is speed times time.

And one that gives us speed, which is distance travelled divided by time.

So congratulations for reaching the end of the lesson, and hope to see you again in future ones.

Bye.