Lesson video

Hi, my name is Mrs. Dennett and in this lesson we're going to be using and applying the speed formula.

We're told that a train travels 475 kilometres in five hours.

There it goes.

We want to find its speed in kilometres per hour.

What is kilometres per hour? This is a compound measure of speed.

We have a measure of distance, kilometres, and a measure of time, hours, and this tells us how far its travelled per one hour.

So let's work that out.

The train travels at 475 kilometres in five hours.

How can we find how far it travels in one hour? We divide the five hours by five, so we do the same to the distance.

475 divided by five is 95 kilometres in one hour.

So the speed of the train is 95 kilometres per hour.

Let's think about the measure of speed more generally.

A car travels d kilometres in t hours.

What is its speed in kilometres per hour? If it travels d kilometres in t hours, we have to divide by the number of hours, t, to get the distance travelled in one hour.

So we also divide the distance by t to find the speed.

The general method is to calculate distance divided by time.

Distance divided by time, and in this example our compound units are kilometres per hour.

Another way that I like to remember the formula is by using the units kilometres, which is a distance.

Per of a line means divide, and hours is a unit of time.

So this helps us to remember that speed equals distance divided by time.

Let's see what happens if the units are different, so not kilometres per hour.

If a car travels d miles in t minutes, what units would we use for the speed? The general formula says to divide the distance by the time.

When we do this, we get d divided by t miles.

So t divided by t will give us one minute.

And d divided by t miles per minute.

We write it like this.

d divided by t miles in one minute, d divided by t miles per minute, so the speed is distance divided by time miles per minute.

In this question we have a runner who runs 150 metres in 30 seconds.

We want to work out the runner's speed in metres per second.

150 metres in 30 seconds.

Divide the time by itself to get one second and then do the same for the distance.

150 divided by 30 is five, so that's five metres in one second.

We write it like this, speed equals five metres per second.

Here are some questions for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

You just needed to calculate the distance divided by the time taken.

The speed is measured in metres per second for this question.

Here we have a car that travels 45 miles in 1.

5 hours.

In this question the time is not a whole number, but don't panic.

We know that speed is just distance divided by time.

The distance is 45 miles, the time is 1.

5 hours, so we calculate 45 divided by 1.

5, which gives us 30 miles per hour.

We can also use the speed distance/time formula to calculate the time taken or the distance travelled.

So a car travels 50 miles at a speed of 20 miles per hour.

How long did the journey take? Let's write down our formula.

We're told the distance is 50 miles.

The speed the car travelled at is 20 miles per hour.

Put these values into the formula and rearrange to find the time taken.

We divide the distance by the speed to find the time taken, which is 2.

5 hours, because the car was travelling in miles per hour.

Here's a question where we want to find the distance travelled.

Write down the formula and then look at the information that we've been given.

A car travels for 3.

5 hours, that's the time, at a speed of 50 miles per hour, that's the speed.

Put these values into the formula and rearrange.

We multiply the speed by the time to work out the distance travelled.

This is 175 miles, as the car is travelling in miles per hour.

Here are some questions for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

We have a mixture of units for speed to think about here, and you need to think carefully about how to rearrange the formula to find the missing value.

In the last question the speed is given in miles per hour, but the time is given in minutes, so you need to change 30 minutes into hours, dividing by 60 to get 0.

5.

So that's 0.

5 hours.

Multiply 30 by 0.

5 to get 15 miles for the distance travelled.

Here are some questions for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

Notice, in question three you're asked for an average speed.

Do you know why? Well, this is because at different stages of its journey the lorry may have been travelling slower than 36 miles per hour.

For example, due to a traffic jam, or having to stop due to traffic lights.

And in the other stages it would have been travelling faster than 36 miles per hour, perhaps on a clear stretch of motorway.

That is why the speed is an average for the whole journey.

So Susan, in the next question, the first part of her run takes 0.

5 hours and the second part takes her 1.

5 hours.

So this is two hours all together.

To find her average speed for the whole run, we take the total distance, 7.

5 kilometres, and divide it by two hours to get 3.

75 kilometres per hour.

Here is a final question for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

For this question, as the speed is given in kilometres per hour, we have to change the 45 minutes into hours as well.

To do this, just divide 45 by 60, which is 0.

75 hours.

To find the distance, multiply 18 by 0.

75 to get 13.

5 kilometres.

And for part B, divide the distance you just found by the speed, so that's 13.

5 kilometres divided by three, which is 4.

5 hours, four and 1/2 hours, or four hours and 30 minutes would also be acceptable answers.

That's all for this lesson.

Remember to take the Exit Quiz before you leave.

Thank you for watching.