Hello there.

My name is Mr. Forbes and I'll be leading you through this lesson from the Moving by Force Unit.

This lesson's called Interpreting Distance-Time Graphs, and it's all about looking at graphs and reading information from them in order to describe the movement of objects.

In the lesson, we're gonna look at a range of distance and time graphs.

We're gonna see how they show the movement of objects.

I'm not sure how objects speed up, slow down, or stay at constant speeds, and even show when objects aren't moving.

So if you're ready, let's start.

These are the most important words and phrases we're gonna use in the lesson.

Distance-time graphs you've seen before; they show movement of an object over time.

Average speed is what you calculate at distance divided by time.

It's how fast something's moving.

Gradient is to do with steepness and we'll see a few examples that.

And stationary means not moving.

Here's the definitions of those keywords, and you can return to this point at any time if you're confused about any of them just to check them out again.

The lessons in two parts, and in the first part we're gonna look at the grading of a graph and what that tells us about the motion of an object, how we can use it to find the speed and direction of travel.

And the second part, we're gonna look at the motion of object, which has several phases, different speeds at different times, objects spinning up or slowing down.

So let's get on with the first part and look at what the gradient means.

This graph shows the motion of two different objects, one shown by the black line and one shown by the dashed red line.

And we're gonna use it to find the speed of those two different objects.

So we can find it using the speed equation, speed equals distance divided by time.

So let's do it for both of those graphs.

We'll have line A, line B, and we can read information off the graph for each of them.

So starting with line A, we can read the information for the distance and time there.

Speed equals distance divided by time; it's 10 divided by 10.

That gives us a speed of one metre per second.

For line B, again, we can read information off the graph.

You find that point.

The speed is the distance divided by the time; that's six metres divided by 10 seconds, and that's 0.

6 metres per second.

Here I've got a graph showing you four different objects, all travelling at different speeds.

We can calculate those speeds just as we did before.

The top one's moving at five metres per second, a black line.

Blue dashed line, three metres per second.

The green dotted line, two metres per second.

And the red dot dash line 1.

2 metres per second.

And what you should see from that is the steep the line, the faster the objects moving.

We call that steepness the gradient.

So we have four lines of different gradients there.

This one is the high gradient, faster speeds, the higher gradient, and this one has got the lowest gradient and the lowest speed.

Okay, it's time for a quick check now.

I'd like you to work out which of these objects is moving at the higher speed and which is moving at the lowest speed.

We've got four lines: A, B, C, and D.

So pause the video, work out the answers, and then restart when you're happy.

Welcome back.

Well, if you look at the graphs, we said the highest speed is the steepest line and that's line D.

So D has the highest speed.

And the lowest speed is the shallowest one, the one with the the minimum gradient, and that's line A.

In all the graphs you've seen so far, we've had objects that start zero metres away, but that's not always the case.

An object could start a certain distance away from the point.

So in this graph, I've got an object that's starting five metres away.

The gradient a graph still shows how fast the object's moving though.

In this case, I've got an object moving at one metre per second.

It's distance is increasing by one metre every second, Right, let's have a look at how we can calculate the average speed of an object when it doesn't start at a distance of zero away from us, it starts at some other distance.

To do that, we need to find the change in distance and the change in time.

So here's an object that starts four metres away from us and it travels along for 10 seconds.

We need to identify the change in the distance.

So it moved from four metres away to 10 metres away.

So we can get the change in distance by subtracting the four metres from the 10 metres and that gives us a distance of six metres it's travelled.

So this objects travel six metres.

We also need the change in time.

That's a bit simpler.

If we just look at the bottom, the change in time is 10 seconds.

It travels from zero to 10 seconds.

So, substituting those two values into our equation for speed, speed equals distance divided by time.

The numbers go in and that gives us an answer of 0.

6 metres per second.

Let's see if you can do the same things I've just done.

I'd like you to find the average speed for this toy train.

So you can see the graph there.

And this toy train starts at distance of two metres away instead of at zero.

So pause the video, find the average speed of the train, and then restart.

Okay, you should have followed the same procedure as I did in the previous example.

First of all, you find the change in distance away.

The change in distance here, well it was two metres away when it started and it went up to nine metres, so that's a change in distance of seven metres.

Then you look at the change in time, and again, that's just 10 seconds.

You write up the equation and then substitute the two values in for distance and time, and that gives us an average speed of 0.

7 metres per second.

Well done if you've got that value.

In this graph, I've got an object that's starting 15 metres away from you.

But looking carefully at the graph, you can see something a bit unusual.

There's no change in the distance each second.

It's 15 metres away at zero seconds and it's still 15 metres away at 10 seconds.

What that means is that the object isn't moving.

It's got a change of distance of zero metres each second.

We call those objects stationary objects.

So this object is stationary.

Time for another check on what you've learned.

I've got a graph here again, and I'd like you to identify which of the lines represent an object that's stationary, which is an object moving at the highest speed, and which is the object moving at lower speed.

So you can see four lines there: A, B, C, and D.

I'd like you to pause the video, answer those questions, and then restart when you're ready.

Welcome back.

Let's have a look at the object that's stationary first and that is line D.

That's a flat line, it's horizontal.

There's no change in distance away over time.

So that's a stationary object.

The highest speed will be the one with the steepest slope.

So that's line C, that's got the highest gradient.

And the lowest speed will have the lowest gradient, and that's line A.

A distance-time graph can show an object moving towards you.

You can see this object starts 40 metres away from you, but over time it gets nearer, it's sloping downwards.

And you should see the distance reduces by five metres each second until eventually at eight seconds the object is zero metres away, so it's got close to you.

You can still work at the speed of this object by looking at the distance and time information.

It speeds five metres per second because it travels five metres every second.

Okay, time for a check now.

I'd like you to identify which of these object is moving at the higher speed and which is moving at the lowest speed.

So pause the video and make your selection and then restart.

Welcome back.

So let's have a look at the graph.

We're looking for the highest speed.

So what we need though is the steepest gradient and that's line B.

B is the highest speed.

And the lowest speed, the shallowest gradient, and that's line C.

It's time for the first task now.

And I've got a graph here with three different objects moving at different speeds.

I'd like you to find the average speed of the objects.

So we've got A, B, and C there.

I'd like you to find the average speed.

So pause the video, use the graph to find the average speeds and then restart when you're happy.

Welcome back.

Let's find the speed of line A.

So line A, we use the average speed equals distance divided by time equation.

And we identify those two values.

We've got a distance of nine metres and a time of 10 seconds.

So putting them into the equation gives us an average speed of 0.

9 metres per second.

Well done if you've got that.

For line B, again, we use the same equation.

We identified information from the graph, a time of 10 seconds and a distance of six metres, and that gives us a speed of 0.

6 metres per second.

And finally, line C, write the equation, read the values of the graph, and that gives us a speed of 0.

25 metres per second.

Well done if you've got all those three.

We're gonna move on to the second part of the lesson now, and this is about changing speed and how a graph shows you that the speed of an object's changing.

I've got a graph here actually shows a change in speed.

The change in speeds shown by the change in gradient.

You can see in the first six seconds the distance is gradually increasing up to nine metres, but in the remaining four seconds there's no change in distance.

So if the objects stopped it's stationary.

I can calculate the speeds as I would normally do.

I've got a speed of 1.

5 metres per second.

And then for the second part, a speed of not metres per second.

I've got a graph here that shows the motion of an object in three parts, or phases as we call them, and we can look at each of those phases separately.

And the first part, here, we can see that the object moves six metres in two seconds, and we can use that to calculate the speed, give us the speed of three metres per second.

In the second part, you should be able to tell by now that the object's not moving, the distance away isn't increasing, so the speed is not metres per second and the object is stationary.

The third part's a bit more difficult.

You should actually see that the object moves again, it's distance away is increasing and it increases from six to eight metres, and it does that in a time of five seconds because it moves from five seconds to 10 seconds, and we can use that information if it's moved two metres in five seconds to get a speed again.

The speed's not 0.

4 metres per second.

So in the first section it was moving faster, in the middle section it was stationary, and in the final section it was moving slower.

Okay, I've got a check for you here.

I'd like you to identify which part of this graph is the object stationary and in which part is the object moving fastest.

So pause the video, make selections, and then restart.

Welcome back.

The answer to the first part was B.

It's stationary in part B.

You can see that because the gradient's flat.

It's moving fastest at part C.

It's got the highest gradient, it's the steepest line.

So congratulations on getting those two.

So far we've looked at graphs that are straight lines, but that's not always the case.

You can have graphs like this, and this is a graph showing an object speeding up and the lines a curve.

If you look at the later part of the graph, the last few seconds, you can see that the gradient is very steep, so it's moving at high speed.

And if you look at the early parts of the graph, you can see that the gradient's much shallower, it's moving at a lower speed, though.

Okay, I'd like to check if you understood that.

Here are three graphs showing the movement of an object, and I'd like you to decide which of those graphs would show an object slowing down to a stop.

So think carefully about that.

Like you to pause the video, make selection and restart.

Welcome back.

You should have chosen graph C for slowing down.

If you look carefully at a graph, it's steep at first, meaning it's moving quickly, but they get shallower and shallower and shallower until actually it's flat towards the end, meaning it's slowing down.

Graph B was showing constant speed.

There's no change in the gradient at all.

And graph A was like the previous graph, it's showing speeding up.

Distance-time graphs can also show objects that are moving backwards at different speeds.

Like in this graph, if we analyse each phase, we've got the first one, it's stationary, there's no change in distance away during that part, it always stays at 80 metres away.

In the second section, the objects moving backwards at two metres per second.

And in the third section, moving backwards up one metre per second.

A distance-time graph can tell us a lot about a journey.

So let's have a look at the example.

So imagine I'm driving to the shops.

And as a drive I travel at a constant speed.

So what would that look like on a graph? Well, as I'm going at this constant speed, I'll get a nice straight line like this and I'm increasing the distance away from my house.

I then stop off at the shops.

How would the graph show that? Well, as I'm not moving, my distance away doesn't increase and I've got a flat line like this.

After I finish shopping, I drive back home.

Drive back home a little bit quicker than I drive to the shops; I'm in a bit of a hurry.

So the slope's downwards because I'm getting closer to my own house.

On my way home, I realise I need to stop off at a friend's house.

So I do that and that means that, again, I'm not moving.

So I get a flat line like this.

We can then use the graph to find out information about the journey.

So for example, I can ask the question, "How far away were the shops?" Well, I just need to look at the axis over here and see when I got to the shops I was 2.

5 kilometres away.

I can ask how long did it take to get to the shops? So we can look at the time axis at the bottom here and see that it took me 20 minutes to get there.

And another question, how long did I stay at the shops? Well, I stayed for 15 minutes, from 20 minutes there to 35 minutes.

Then I drove home and that took me 10 minutes.

Well actually I didn't quite get home, did I? I stopped off at a friend's house.

And I can ask the final question, how far away was that friend's house? And again, looking here, I can look across to the distance away axis and see my friend lives 9.

5 kilometres away.

Now we can find the average speed of an object by looking at the total distance it's travelled and the total time it took.

And it doesn't matter how many phases there are in a motion, whether it changes speed or not, we're just finding the average speed.

So I've got a graph here.

Let's draw some lines on it.

And we're gonna try and find the average speed.

And to find the average speed, we just need to look at the total distance and the total time.

So, average distance is total difference divided by total time.

We can identify the total distance it went by looking at the end point of the graph and looking across to the distance axis again.

And we can see that's six metres.

And we can find the total time by looking at the bottom there, looking down from the point.

Substituting those two values in we get average speed is six divided by 10, and that gives us an average speed of 0.

6 metres per second.

Now I'd like you to find an average speed looking at this graph.

So, what's the average speed for that complete journey, please? Pause the video, find the answer, and then restart when you're happy.

Okay, let's have a look at the answer.

The answer is 1.

5 metres per second.

And this is how we get it.

We start with the equation, we find the values from the graph, the average speed is 90 divided by 60.

It travelled 90 metres in 60 seconds.

And we calculate that and that gives us 1.

5 metres per second.

Well done if you've got that.

You can also use a distance-time graph to find the average speed for a section of the graph between two different times.

And that's what I'm going to do here.

I'm gonna find the average speed between two and eight seconds, these points.

I'm gonna use the speed equation for that.

Now you should be able to see from the graph that the object travelled a total distance of eight metres between two and eight seconds.

It was at one metre and then it went up to nine metres, so it went eight metres.

That took place in a time of six seconds.

So I put those two values in the equation.

The average speed is eight divided by six, given an average speed of 1.

3 metres per second.

Okay, you've reached a second task of the lesson, and I'd like you to find some information from this graph.

It shows the movement of a robot toy.

And what I'd like you to do is to add label to the graph to describe the movement of the robot in detail.

And then I'd like you to calculate the average speed of the robot in the first 50 seconds.

So, pause the video, answer those two questions, and then restart when you're ready.

Welcome back.

Let's add the label to the graph.

So looking at the first part, you should be able to find that the speed's 0.

1 metres per second.

The second part of the graph, it was stationary, it didn't move at all.

And the third part, it was moving at 0.

4 metres per second.

And in the final part it was stationary again.

You were asked to calculate the average speed of the robot during the first 50 seconds, and so we can look at the 50 seconds mark, look upwards and find that the distance travel was 10 metres and use that in the equation.

And that gives us an average speed of 0.

2 metres per second.

So well done if you've got that.

You've reached the end of lesson now.

So here's a summary of the information.

You can see I've got a distance-time graph here, and it shows that lower speed is a shallow gradient, high speed as a steep gradient, and a stationary object has no gradient at all; it's gradient of zero.

You can calculate the speed using average speed equals change in distance divided by change in time for any section of that graph.

And if you wanna show backwards motion or motion towards you, you'll have a slope in the opposite direction.

So that's the end the lesson.

I hope to see you in the future ones.

Bye.