Hello there, my name is Mr. Forbes and I'll be guiding you through this lesson on the moving by force units, and it's all about distance-time graphs and how we can read information off them and use that to calculate the speed of moving objects.

By the end of the lesson, you're gonna be able to calculate the speed of an object by reading information off a distance-time graph.

You're gonna need a calculator because you're going to be reading distance information, time information, and performing a calculation based on that that'll give you the speed.

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

This is the set of the important keywords we're going to look at in the lesson.

Distance-time graph, and that's the type of graph we're gonna be looking at.

Axis, scale and division are all parts of a graph and you'll need to understand what they mean.

And then average speed, which is what we're gonna be calculating.

Here's an explanation of those keywords, and you can return to this slide at any point just so you can check up on those keywords if you're confused about them.

This lesson's got two parts.

The first part is all about exploring the graphs, understanding what they mean.

So we'll look at what the parts of the graph are and how we can take values off the graph, and then how we can use those values to calculate speed.

In the second part, we're gonna start looking at how the graphs can represent motion over time, how we can see an object's movement pattern in those graphs.

So we'll start with the first part, finding speed information on a graph.

Okay, this is a typical distance-time graph.

We're gonna spend a few minutes looking through the features of the graph so you understand them properly.

Okay? The first thing you need to be able to identify are two axes.

The axes are the vertical and horizontal lines along the bottom and side of the graph.

So this is the horizontal axis, and in a distance-time graph this represents the time value.

Okay, so you can see the time seconds is labelled on it.

The vertical axis on the distance-time graph represents the distance an object has moved, and that again, you can see there, is measured in metres on this graph.

The axes on a graph have got a set of scales on them, and the scales are the numbers that are on there and they tell us information about the maximum and the minimum values that the graph can show.

The scales on the graph usually start at naught, but not always.

You have to watch out for those in later lessons.

These ones do start at naught, and they go upwards towards a maximum.

So you can see on the time axis it goes from naught to six, which is the maximum time, and the distance axis, it goes upwards from naught to five, which is the maximum distance that this graph can show.

Okay, there's the maximum time, six seconds, and there's the maximum distance, five metres.

The scales on the graph don't just have the maximum and the minimum values, they have a set of divisions on them.

And the divisions are usually blocked up in sections of one, two, five or 10.

And they allow us to see values on the graph more clearly.

I've got this scale, the time scale here, and that's got the division of one.

It goes naught, one, two, three, and so on, all the way up to six.

And the distance scale on this graph, and it's got divisions that go up in tens.

Goes 10 metres, 20 metres, 30 metres, 40 and 50, and they're equally spaced along the axes, so you get this grid pattern.

Okay? On the graph we also draw this set of horizontal and vertical lines called grid lines, and they allow us to read values off the graph more easily than if it was just a dot on a white sheet of paper.

We can look along and down those lines to see values on the scales.

Okay, a first check of your understanding.

I'd like you to look at this graph carefully and tell me which part of it is missing.

Is it the time axis, the time scale, the distance axis or the distance scale? So pause the video and select your answer and then restart when you have.

It was the time scale that was missing from the graph.

There's no numbers along the bottom axis there, so we can't read any time values off it.

So it's not particularly useful graph.

Okay, a second check for you here.

I'd like you to tell me what the divisions are for the distance scale on this distance-time graph.

Is it naught-point-five-meter increments it goes up in, one-meter increments, two-meter increments or 12-meter increments? Pause and make your selection and then restart.

Okay, the answer to that one was it's two metre increments.

You can see it goes from naught to two, then from two to four, which is an increase of two again, from four to six, six to eight, and so on.

So it's two-meter increments on that scale.

Okay, what we're gonna do is we're gonna try and read information from a graph.

I've got a fairly simple graph here, a distance-time graph with one point plotted on it.

And what we're gonna do is use the scales and the axes to read information about it.

So this is the point here, and what I want to do is I want to determine what the time is at that point, how long has that object been moving for? And to do that, all I need to do is to find a point and look directly downwards to the time axis, and that will give me the time.

So I'll look downwards there and it's five seconds.

That object has been moving for five seconds.

To find the distance it's travelled, I can look across towards the distance axis, like this.

That's been moving for five seconds and it's travelled four metres.

So I've read the distance and the time for that particular object, and I can use that information to calculate speed.

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

I'd like you to use this graph to find the time and the distance for that object.

So use the same processes I've just used and find the time and distance.

So pause this video and then restart once you've selected.

Okay, so having a look at that, we've got a time of three seconds.

Looking directly down from the point gives us the time of three seconds, and looking across from the point gives us a distance of four metres.

So well done if you got both of those values.

As I mentioned before, we can use the information from the distance-time graph to calculate speed, we just have to read off the time and the distance and then use that in the equation.

So looking at this graph, you can see the time is four seconds, you can see the distance is five metres, and putting that into the speed equation we get speed equals five divided by four, giving us a speed of 1.

25 metres per second.

I've got a check here for you to try the same thing.

I'd like you to find the speed of this object.

So pause the video, find the speed, and then restart when you're happy.

Okay, so let's have a look at the graph.

We find the time, we're looking down, three seconds, we find the distance looking across, four metres, and that gives us a speed of 1.

33 metres per second.

Well done if you found that.

So far the graphs we've looked at have been fairly simple in that they've just got lines on the particular numbers, but most distance-time graphs have subdivisions, and subdivisions are ways of breaking down the axis so we can read values off it to a smaller precision.

This graph has got a set of subdivisions.

The subdivisions are usually in multiples of two, five or 10.

In this case there's five subdivisions, and if you look perfectly at the time axis you can see each subdivision is naught point two seconds.

I've split up that one second gap between one and two into five parts, and each part is naught point two seconds long.

Those subdivisions allow you to read smaller values.

So you can read things like 2.

5, 2.

4 off the graph and not at the nearest whole number.

So for my example here, reading the value of the time for that point, I can actually read it as 3.

6 seconds.

It's beyond the three second mark and three more subdivisions along, and each of those subdivisions is naught point two seconds, so that's 3.

6 seconds, the time.

Similarly for the distance, it's just above four, so it's four point something, and each subdivision is 0.

2 of a metre, so that's 4.

2 metres.

So I'm reading the information more precisely now as I've got those subdivisions.

Okay, here's an example for you to do.

I'd like you to find the speed of this object using the subdivisions of the graph.

So pause the video, find the speed, and then restart when you're happy.

Well, welcome back.

Let's have a look at that.

We can find the time by looking downwards from the point using the subdivisions, it's 2.

4 seconds.

We can find the distance by looking across from the point, that's 4.

8 metres.

Putting that into the equation, speed equals distance divided by time, gives us an answer of two point naught metres per second.

So congratulations if you got that.

Now it's time for the first task of the lesson.

I'd like you to find the speed of these three different objects.

There's three objects there, A, B, and C.

I'd like you to find those speeds using the graph.

So pause the video, find the speeds, and then I'll work through the solutions with you afterwards.

Okay, let's have a look at the results here.

We can look at Object A first, writing down the equation.

We need to find the distance and time, so we look down and across, find the values and put them in, and that gives us a speed of two point naught metres per second.

Moving on to Object B.

Same thing again, speed's distance divided by time.

Find the values from the graph, and that gives us an answer of naught point seven metres per second.

And finally, point C.

Speed equals distance divided by time, put the values in, naught point six metres per second.

Congratulations if you got those three answers.

Okay, we're on to the second part of the lesson, this is the patterns of motion part, and we're going to use the graphs to try and describe what's happening over a period of time.

Not at one particular time, but over several seconds.

Okay, I've got a graph here showing the position of an object at different times, so the distance away from somewhere at different times, and it's the same object every time.

This isn't a separate set of objects, it's just one object and we've measured its distance at different times and plotted that on a graph as a set of points, okay? And what it does is it shows us how much the object is moving.

You can see the series of points here, at two seconds it was one metre away, and so on, all the way up to at 10 seconds it was five metres away.

Now this object is moving at a constant speed, and we can see it's moving at constant speed by looking at how far it moves each second.

In the first second, we can look at the distance increase.

In one second, its distance increased by three metres, and then we can look in the second second, between one and two there.

And again, in that one second amount of time it's gone three metres again.

And in the next second of time, three metres, and so on.

And as you saw earlier, this is a pattern that shows constant speed.

The speed of this object is three metres every second, three metres per second.

So to check your understanding of reading information from graphs, I'd like you to answer this.

I'd like you to fill in the missing numbers in these sentences that describe the motion of this single object.

Okay, between naught and two seconds, the distance has increased by how many metres? And between six and 10 seconds, the distance has increased by how many metres? So pause, fill in those gaps and restart please.

Okay, so checking your answers, we have these two points we can compare to look at the pattern.

Between naught and two seconds, we can see the distance has increased by one metre, so we fill that in.

And for the second one, between six and 10 seconds, the distance has increased by two metres.

So the answer to the second one is two metres.

Well done if you got both of those.

So here's the second example, and again, I'd like you to fill in the blanks by analysing the graphs.

So, the object has travelled the first three metres in how many seconds, and then the object travelled from three metres to five metres in how many second? So I'm checking if you can read time information from the graph.

Pause the video, then restart once you've got your answers.

Great, we're back.

Let's have a look at those.

And for the first one, in the first three metres we can look across and see how long it took to get to there.

That is six seconds if you look downwards.

And the second one, it travelled from three metres to five metres.

So we find the three metre point and the five metre point, and we look down there and we can see that that's a time of four seconds it took to move between those two points.

So that's four seconds.

Well done if you got those two.

Okay, so far what we've done is looked at single points on a graph, but distance-time graphs, they're usually graphs that show more information.

They show the complete movement of an object at any particular time.

And to do that we use lines on the graph.

So here we've got a graph with a single point on, but rather than that, I'm gonna draw a line between the points, and that line shows the pattern of movement for that object, assuming it's moving at a constant speed during those times.

So that line can then be used to find the distance and the time at any particular moment.

So we look at that and we can say, at two seconds, the distance it travelled when we look up from two seconds, and find the distance, four metres.

We can look at three seconds and see how far it's travelled at that point.

Looking up from three seconds and across gives a distance of six metres, and so on.

So we can see a range of different distances at different times that fit this pattern.

Five seconds, it distances 10 metres.

So let's see if you can read some information from a graph.

I'd like you to look at this graph and tell me, how far has that object moved after 2.

5 seconds? Is it 16 metres, 10 metres, eight metres or 2.

5 metres? Pause the video and restart once you've got an answer.

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

Eight metres.

If you look up from 2.

5, so we've got to use the subdivisions there, looking up from 2.

5, you can go across and find the distance is eight metres.

Well done if you found that point.

We can also use the graph to find out how long it took to move certain distances.

So we've got a graph again here.

We'll make it into a line graph, a straight line connecting those two points, and for a constant speed.

And we can look at how long it took to move 10 metres.

So what we do is we find 10 metres on the distance axis, we look across and then we look down to find the time it took to get to that distance, and that's five seconds.

Again, we can look at another distance, let's say seven metres.

To move seven metres, we look across from seven metres, we've got to use the subdivisions here, and then we look downwards and we find that's 3.

5 seconds.

So it took 3.

5 seconds to move seven metres.

Okay, we're on to the final task of the lesson.

I've got a graph here for you to analyse, and I'd like you to find four different things for me please.

I'd like you to find the average speed of this object by taking information from it.

I'd like you to find the distance the object travels in the first four seconds, the time it takes the object to travel three metres, and the distance the object moves between two seconds and five seconds.

So look through all that, pause the video and try and answer those four parts, and I'll be back with you when you're ready to start again.

Okay, the first of those questions here, we're finding the average speed of the object.

We take some values from the graph.

We go across nine metres in six seconds.

Putting that into the equation, we get a speed of 1.

5 metres per second.

Okay, the second of those, we look up from four seconds to find a distance of six metres.

The third, we look for three metres, look down, and that gives us two seconds.

And finally, the distance the object moved.

And you can see there, we find the two different distances and subtract them to give a distance of 4.

5 metres.

So congratulations on getting those.

Okay, we've reached the end of the lesson now, and here's a summary of the information about distance-time graphs.

A distance-time graph shows how an object has travelled at different times.

We have two axes, a horizontal axis showing the time and a vertical axis showing the distance, as shown in the figure there.

We've got scales that give the maximum and minimum, and divisions along the the axes that will tell us the values in between, and we can even have subdivisions there.

And we draw lines on the graph to show objects moving at constant speed.

So that's the end of the lesson.

Thanks for taking part with me and I'll see you in a future lesson.