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Hi, I'm Miss Kidd-Rossiter, a maths teacher from Hull, and I'm going to be taking today's lesson on displacement-time graphs.

It's the first lesson of two.

Before we get started, make sure you're in a nice quiet place, where you're free from all distractions.

You've got something to write with and something to write on and a ruler might be helpful for today's lesson as well.

If you need to pause the video to get any of that sorted, then please do.

If not, let's get going.

So, try this, this graph shows the distance Xavier is from home throughout a day.

So, we've got distance here on the y-axis, and we've got the time of day on the x-axis.

Compare what is happening at each of the marked segments.

So, this is segment A, segment B, segment C, segment D and segment E.

And what could he be doing? Pause the video now and have a go at this task.

Excellent, what did you think? So, this is the distance from Xavier's home on the y-axis.

So, if we look at section A of the graph, he's slowly getting further away from home and the time is going up, isn't it? Then, he suddenly arrives somewhere, at this point, because the distance doesn't go up anymore, does it? So, it means that he's staying in the same place for a little while as the time continues on.

Then, in section C, this is a steeper line than in part A, so he's coming back towards home at a faster speed.

D, he stops somewhere again, and then E, he continues back to home.

So, you could have thought of a story to go with this.

So, this is what we call a displacement-time graph, Displacement-time, and the key difference between a displacement-time graph, and a distance-time graph is that it shows you the direction of travel, so it's distance from home rather than just distance travelled.

So let's have a look at another example together.

So, the distance-time graph or, we should say, the displacement-time graph, shouldn't we, shows the journey of a man from Durham to Edinburgh and back, so he's leaving, he arrives in Edinburgh here, and then he comes back to Durham in this last segment here.

I want you to pause the video, and think about the three questions that are on the right-hand side of your screen, and make sure to explain your answers.

When you're ready to talk about them, resume the video.

Excellent, let's talk about the first one together, then.

How far is the journey from Durham to Edinburgh? Well, we're told that the displacement-time graph shows the journey of the man from Durham to Edinburgh and back.

So, he must be leaving from Durham and going to Edinburgh.

So, the distance is 250 miles.

How long did the man stop in Edinburgh? Well, to do this, it's this part here where his distance away from Durham doesn't change.

So, we can read down, he gets to Durham, sorry, he gets to Edinburgh at 11:00 AM, and he leaves Edinburgh at 12 noon.

So, how long does he stop, exactly one hour, perfect.

And then finally, did he travel at a faster speed going to Edinburgh or on the return journey? So we've seen, haven't we, that speed is equal to the distance divided by the time.

So, on the outward journey, that's going to at Edinburgh, his distance is 250 miles, and his time is two hours.

So, that indicates that his speed was 125 miles per hour.

And on the return journey, he travels 250 miles, but the time, this time, is three hours.

So, 250 divided by 3 tells us, that his speed is 83.

3 recurring miles per hour.

And remember, these are average speeds.

You're now going to apply your learning to the independent task, so pause the video here, navigate to the independent task.

And when you're ready to go through some answers, resume the video, good luck.

How did you do on the independent task? Let's go through it together.

So, which part is section A here? Exactly, it's moving slowly at a constant speed, well done.

Part B is moving rapidly away from the starting point at a constant speed, we know the steeper the line the quicker the speed.

Part C is not moving, and then part B is moving at a constant speed back towards the starting point.

We've got a journey of a cyclist from Birmingham to Coventry here.

What time did the cyclist leave Birmingham? Well, we can see that on the x-axis here, the time was 10:39, each of the little increments on this graph is worth three minutes.

The cyclist arrived in Coventry at 12 o'clock.

How far is Coventry from Birmingham? Now, this is not a perfectly accurate graph and scale.

So, if you got something around 18 miles, that's absolutely fine.

You can see it's actually slightly less than 18.

So, I think anything between 17 1/2 and 18 miles would be perfect here.

The cyclist made one stop on his journey.

At what time did he stop? Well, we can see that he stopped at this point here.

So, let's read down, and that is 11:15.

And how far was the cyclist from Coventry when he stopped? So, we're looking for, this is Coventry here, so we're looking for that amount of distance.

So, it's about three miles, so anything between two and a half and three miles is perfect there.

I hope you wrote some lovely stories for these graphs.

So, the first one here could've been anything.

So, it could've been someone going to one shop, they couldn't find what they needed.

So, they walked back towards home and went to another shop, and that shop didn't have what they needed either there, so they went to a third shop, and they stayed here longer because they found that they did have what they needed and they had to queue up, and then they came home.

The second one could've been a race, where you've got one person starting really quickly and then getting out of breath and having to wait and then improving a little bit, so going a bit further and then having to stop again and then going towards the end, and who would've won? So, looks like here, what everyone had to have a stop in the race, so maybe it's not a realistic graph for a race.

What did you come up with? Finally, then explore task, these displacement-time graphs show the journeys of two different cars, which is more realistic and why? Pause the video now, and think about that.

I would say this one is more realistic because it shows gradual acceleration and deceleration, doesn't it? We don't have an instant change in speed when we're driving, you can't go straight away from 0 to 60 miles an hour.

It takes anywhere between 4 and 12 seconds to get to that speed.

So, this one is a more realistic representation.

That's the end of today's lesson.

So, thank you so much for all your hard work.

I hope you've enjoyed looking at displacement-time graphs.

We're going to look at it in a bit more depth next lesson.

Before you go, don't forget to take the end of lesson quiz, so that you can show me what you've learned and, hopefully, I'll see you again soon, bye.