Lesson video

Hi there, my name is Ms. Lambell.

You've made a superb choice deciding to join me today to do some maths.

Let's get cracking.

Welcome to today's lesson.

The title of today's lesson is converting between metric speed measures, and that's within the unit, Compound Measures.

No surprises, by the end of this lesson, you'll be able to convert between metric speed measures.

Speed, obviously, is going to be something we're going to be talking about a lot during today's lesson, so a quick recap as to what we mean by speed.

Speed is the rate at which something is moving.

It is measured as the distance travelled per unit of time.

Today's lesson is split into two separate learning cycles.

In the first one, we will look at converting metric measures involving speed, and in the second one we will look at comparing using speed, distance, and time.

Let's get going with that first one, converting metric measures involving speed, let's go.

The fastest land mammal is a cheetah.

A cheetah's top speed is 29 metres per second.

Remember, m/s is our unit of speed and it represents metres per second.

Would a cheetah break the speed limit of 110 kilometres per hour on a dual carriageway in France? The speed limit on a dual carriageway in France is 110 kilometres per hour.

We are going to work out whether if a cheetah was running at top speed, whether it would break this speed limit.

We've got our time, we've got our distance.

Our speed was in metres per second, so I know that in 1 second, I travel a distance of 29 metres.

Well, I don't, the cheetah does.

We now need to scale this up to look at what that is in kilometres per hour.

I'm going to start by looking at how many metres per minute.

What's my multiplier that takes me from 1 second to 1 minute? And that's multiply by 60.

If I multiply the time by 60, I must multiply the distance by 60, because they are directly proportional to each other.

Therefore they have a constant multiplicative relationship.

29 multiplied by 60 is 1,740 metres.

We are converting into kilometres per hour.

I'm now going to work out what that would be in 1 hour.

What's my multiplicative relationship that takes me from minutes to hours, and that's multiply by 60 again.

There are 60 minutes in an hour.

I multiply my distance by 60, giving me 104,400 metres.

Now we're almost there.

We've got how far we would go in 1 hour, but the speed limit is in kilometres per hour and we have our distance in metres.

So our final step is going to be to convert 104,400 metres into kilometres.

And how do I change metres into kilometres? Yeah, that's right, I divide by 1,000.

This time I'm only dividing the right hand side by 1,000 because I'm just converting between metres and kilometres and this gives me 104.

4 kilometres.

The cheetah's speed is 104.

4 kilometres per hour, therefore it does not break the speed limit.

I wonder if you thought it was going to break the speed limit or whether it wasn't and whether you were right with your answer.

A car is travelling at an average speed of 50 kilometres per hour.

What is its average speed in metres per second? Again, we're going to use a ratio table.

This time I need to convert from kilometres per hour into metres per second.

So in 1 hour we are going to go 50 kilometres.

In 1 minute then, how far will we be able to travel? There are 60 minutes in an hour, so I need to divide by 60.

If I divide the time by 60, I must divide that distance by 60 because of that proportional relationship.

I'm going to leave that as a fraction 50 over 60 because it's a recurring decimal and I'd rather have my answer as an exact value.

I now want to work out, but remember, we're working towards metres per second, how many seconds are in 1 minute? 60, so I'm going to divide by 60.

I'm going to do the same thing to the distance, which is 1 over 72 kilometres.

So 50 over 60 divided by 60 and then that simplifies to 1 over 72.

We wanted the average speed in metres per second and we've actually got it in kilometres per second.

I now need to convert kilometres into metres.

How do I do that? That's right, I multiply by 1,000.

1 over 72 multiplied by 1,000 is 13.

9.

A car that is travelling an average speed of 50 kilometres per hour is travelling at an average speed of 13.

9 metres per second.

During qualifying for the 2016 Grand Prix of Azerbaijan, Valtteri Bottas achieved an incredible top speed of 378 kilometres per hour.

And this is currently, well when I wrote this, the highest top speed recorded in Formula 1.

What was the speed in metres per second? How many metres can that car cover in 1 second? Let's start with our speed.

We know the top speed is 378 kilometres per hour, so in 1 hour we would travel a distance 378 kilometres.

Let's work out a minute.

There are 60 minutes in an hour, so I'm going to divide by 60, gives me 6.

3 kilometres, so in 1 minute we would travel 6.

3 kilometres.

That seems insane, doesn't it? We're working towards a speed in metres per second.

How far would we go in 1 second? 1 second is a 60th of 1 minute, so we're going to divide by 60.

This means we would go a 60th of the distance.

So 6.

3 divided by 60 is 0.

105 kilometres.

The speed we wanted though was in metres per second, so our time is in seconds.

We now need to convert our kilometres into metres and we're going to do that by multiplying by 1,000, 105 metres.

The car was travelling at a speed of 105 metres per second.

Just think about that moment.

Think about a 100 metre track, if you do that in PE and it travels that in 1 second, sort of blows my mind a little bit.

Now you can have a go at this check for understanding for me.

The fastest confirmed speed of an ostrich is 17 metres per second.

The speed limit on a road is 60 kilometres per hour.

Does the ostrich break the speed limit? I've given you the table there.

If you need help with how to set it up, I'd like you to fill in the distances and then decide whether the ostrich breaks the speed limit.

So as always, not just yes or no, I need to see that table of completed values to support your answer.

Pause the video and then when you are ready come back and we'll check and we'll see whether the ostrich did break the speed limit.

Let's take a look then.

In 1 second we are travelling 17 metres and we get that from the speed, 17 metres per second.

We're going to multiply that by 60 to work at how far we will go in 1 minute, which is 1,020 metres.

We then multiply that by 60 to work at how far we are going to go in 1 hour, which is 61,200 metres, but we want the speed in kilometres per hour.

We are going to divide 61,200 metres by 1,000, giving us 61.

2 kilometres, the ostrich is travelling at speed of 61.

2 kilometres per hour.

Therefore it does break the speed limit, though we'd be a bit scared if we saw an ostrich, wouldn't we, running along the road.

A person ran 1.

2 kilometres in 10 minutes.

What was the speed in metres per second? Here's Lucas' workings, and here's Jacob's workings.

I'd like you to look through the two methods and decide what has happened at each of the steps.

So pause the video and check that you understand what has happened at each step and why.

I'll be here waiting for you when you get back.

Like I said, you can pause the video now.

Let's take a look at Lucas' workings.

We started off with the information given in the question.

1.

2 kilometres in 10 minutes, then divided by 10 to work out the number of kilometres that was per minute, then divided by 60, this works out the number of kilometres per second, and then multiplied by 1,000 because we are converting from kilometres per second into metres per second.

We'll compare that now with Jacob's method.

Jacob also starts with 10 minutes and 1.

2 kilometres obviously, 'cause that's given in the question.

Firstly, he's multiplied by 60 and this converts minutes into seconds.

10 minutes in seconds is 600 seconds.

He's then multiplied by 1,000.

This is converting the kilometres into metres.

So in effect he's done two steps in one there.

We've then divided by 600 and that's given us the number of metres per second so we can see that we are travelling at a speed of 2 metres per second.

Which of those methods do you prefer? Now obviously there's no right or wrong answer to that and there are also many other ways of getting the answer of 2 metres per second.

Sofia's smart-watch tracks her walk to school.

What was her average speed in kilometres per hour for her slowest part of the journey? Which part of her journey was slower? The first part, as that line has a shallower gradient, remember, the shallower the gradient, the slower the speed.

This part of the graph I've highlighted shows the slowest part of her journey.

We can see from this that she walks 250 metres in 5 minutes.

We can now scale this 5 minutes.

We cover 250 metres.

I want to know my speed in kilometres per hour.

There are 60 minutes in an hour.

My multiplier that takes me from 5 to 6 is multiply by 12, 250 multiplied by 12 is 3,000.

We wanted to know the speed in kilometres per hour.

We've got 60 minutes is 1 hour.

We just need to convert our 3,000 metres into kilometres, which is 3 kilometres.

Sofia, or the slowest part of her journey, her average speed was 3 kilometres per hour.

Now let's have a go at task A.

You're gonna convert the following speeds, and if appropriate, give your answers to two decimal places.

I've given you there the tables to help you get started on these questions.

The speed of the sailfish is 8.

3 metres per second.

What is the speed in kilometres per hour? The speed of a helicopter is 285 kilometres per hour.

What is the speed in metres per second? Pause the video and then come back when you're ready.

And part C and D, the speed of a snail is 0.

013 metres per second.

I'd like to convert that into kilometres per hour.

And the speed of a plane is 900 kilometres per hour and I'd like you to convert that into metres per second please, again, pause the video and then come back when you're ready.

And question number 2, calculate Sofia's average speed in kilometres per hour for the fastest part of the journey.

Pause the video and then come back when you're ready.

There are our answers.

If you need to, you can pause the video and check each line of the table.

I'm just going to read out the speeds.

A, the speed of the sailfish is 29.

88 kilometres per hour.

B, the speed of the helicopter is 79.

17 metres per second.

C, the speed of the snail is 0.

047 kilometres per hour.

And D, the speed of the plane is 250 metres per second.

Calculating Sofia's average speed for the fastest part of the journey, so we can see that it was 750 metres and took 6 minutes.

Her average speed was therefor 7.

5 kilometres per hour.

Now we'll move on to the second learning cycle, comparing using speed, distance, and time.

The average speed of an elk is 72 kilometres per hour.

The average speed of a coyote is 19.

4 metres per second.

Which is faster? Just looking at those, which one do you think is faster? Just a bit of fun to see whether you get it right.

I've made my decision.

We can convert the elk's speed into metres per second.

In 1 hour we travel a distance of 72 kilometres, so in 1 minute, I'm dividing by 60, I would travel 1.

2 kilometres.

I want to know how far then I would go in 1 second.

So I'm gonna divide by 60, giving me 0.

02 kilometres.

So in 1 second my final step is, convert 0.

02 kilometres into metres by multiplying by 1,000 and I get 20 metres.

This means that 72 kilometres per hour is equivalent to 20 metres per second.

So we can see that the elk was faster.

Did you decide the elk was faster? I got it wrong, I thought it was going to be the coyote.

We could also have converted the coyote's speed into kilometres per hour.

So let's just have a look at how we would've done that.

We know that our speed is 19.

4 metres per second, so in 1 second we cover a distance of 19.

4 metres.

Firstly, we need to scale this up to work out how far we are going to go in an hour.

So I decide to do this by working out a minute and then an hour.

60 seconds in a minute, so in 1 minute we will travel a distance of 1,164 metres.

Now let's look at an hour.

There are 60 minutes in an hour, so I'm gonna multiply by 60.

In 1 hour we would travel 69,840 metres.

So in 1 hour I was trying to work out my speed in kilometres per hour.

So I'm gonna divide by 1,000, because that will give me metres as kilometres, which is 69.

84 kilometres.

19.

4 metres per second is equivalent to 69.

84 metres per second.

And again, we can see that the elk is faster.

Which is faster, travelling 15 kilometres in one third of an hour or 12 metres per second.

I'd like you to take a look at these tables, which of them can be used to answer this question.

Pause the video, look through them each carefully like we did earlier, check you understand what is happening at each step and why, and decide which of those four tables can be used to answer the question, which is faster.

Pause the video and then when you've got your answer, come back.

What did you decide? Actually, all of them can be used to answer this question.

Let's take a look at this first table.

What's happening at each step in this table? What did you decide when you looked at this table? The first step is a conversion of one third of an hour into minutes.

One third of an hour is 20 minutes, then the speed in kilometres per minute, followed by the speed in kilometres per second, and then the speed in metres per second so that we could compare it to the 12 metres per second.

What did you decide for this table? What was happening at each step? Let's take a look.

Step 1, there was a conversion of kilometres into metres.

15 kilometres is 15,000 metres.

Then the speed in metres per hour was found, followed by the speed in metres per minute.

And then finally the speed in metres per second, allowing us to compare 12.

5 metres per second to 12 metres per second.

And what about this one? Could you see what was happening at each step here? We'll take a look.

This time we've started with 12 metres per second.

Next we find the speed in metres per minute, followed by the speed in metres per hour.

That was followed by the speed in metres for one third of an hour.

And finally the speed in kilometres for one third of an hour, allowing us to compare 14.

4 kilometres in one third of an hour to 15 kilometres in one third of an hour.

And the final table, what was happening here? Again, this one started with 12 metres per second.

There was a conversion of metres to kilometres and the distance in kilometres per minute that just happened in one step.

Then the speed in kilometres per 20 minutes, which is one third of an hour.

And again, this allowed us to compare 14.

4 kilometres with 15 kilometres.

There are lots and lots of different ways of converting between these measures of speed.

You just need to find the one that you feel most confident with.

Now for task B, you're gonna convert the following speeds.

A, 20 metres per second into kilometres per hour, B, 63 kilometres per hour into metres per second, C, 132 metres per second into kilometres per hour, and D, 189 kilometres per hour into metres per second.

Pause the video, remember the table to help you set out your work in a clear and concise way.

I'll be waiting when you get back.

Question number 2, Concorde's maximum cruising speed was 2,179 kilometres per hour.

The NASA x-43 experimental plane's top speed was 3,292.

8 metres per second.

I'd like you please to calculate the difference between the two speeds in metres per second, and you're going to give your answer please to 1 decimal place.

Pause the video, come back when you've got your answer.

Question number 3, is Andeep correct? And you must show how you got your answer.

55 kilometres per hour is faster than 15 metres per second.

Decide how you're going to answer this question and then come back when you've got an answer.

But don't forget, you must show your tables to show me how you got that answer.

Pause the video now.

Question 4, which is faster? Travelling 12 kilometres in two thirds of an hour or 5 metres per second.

And again, you must show how you get your answer.

Pause the video now.

I'll be waiting for you to check those answers when you get back.

Now let's check our answers.

A, 72 kilometres per hour, B, 17.

5 metres per second, C, 475.

2 kilometres per hour, and D, 52.

5 metres per second.

Question 2, the difference between the two speeds is 2,687.

5 metres per second, and there's the table there of converting Concorde's speed into metres per second.

Obviously, if you need to, you can pause the video and check each of your steps.

Question 3, you may have decided to convert kilometres per hour into metres per second or metres per second into kilometres per hour, and we can see that Andeep is correct.

And finally, question number 4.

12 kilometres in two thirds of an hour is equivalent to 12 kilometres in 40 minutes, which is 18 kilometres per hour, and that's 5 metres per second, so they were the same speed, exactly the same speed.

I wonder if you got that.

Now let's summarise our learning from today's lesson.

Using a step-by-step approach to convert between metric speed measures is the most useful and also the most successful, as an example there of one that we looked at during the lesson.

You may need to convert speeds from distance time graphs.

Here's the example we looked at when Sofia's smartwatch was tracking her walk to school, and we could use that and the table to work out the average speed was 3 kilometres per hour.

Great work today.

I really enjoyed working through all these concepts and maths with you.

Hopefully I'll see you again really soon.

Take care of yourself, goodbye.