Lesson video

Hello there.

I'm Mr. Forbes, and welcome to this lesson from the Measuring and Calculating Motion unit.

In it, we're gonna be looking at calculations from motion graphs, and that involves using the graphs to find things like final displacement, distance travelled, speed, and acceleration.

By the end of this lesson, you're gonna have looked at a wide range of motion graphs and be able to take readings from those graphs to calculate things like distance, displacement, speed, velocity, and acceleration.

You'll also be able to convert from one graph to the other through a series of calculations.

Here are the key words that will help you understand the lesson.

First on the list, displacement-time graph, and that's a type of graph that shows the displacement of an object over a period of time, where displacement is how far it is from its starting position.

There's also a velocity-time graph, which shows the velocity of the object over the period of time.

Then there's velocity, and velocity is the rate of change of displacement, how fast the displacement is changing.

And finally, acceleration, and the acceleration of an object is the rate of change of velocity, how much the velocity is changing each second.

And here's some explanations of those keywords that you can return to at any point in the lesson if you need some help.

In the first part of the lesson, we're going to be comparing the two types of motion graph: velocity-time graphs and displacement-time graphs, and we'll see what type of information we can get from both.

In the second part of the lesson, we're going to be looking at one graph and trying to convert information we can obtain from it into the other type of graph.

So, we'll take a velocity-time graph and use it to make a displacement-time graph, or a displacement-time graph and use that to make a velocity-time graph.

And in the third part of the lesson, we're going to find information from both types of graphs and use that in a variety of calculations.

So, when you're ready, we'll begin by looking at the two types of motion graph.

Displacement-time graphs and velocity-time graphs both look very similar and give us similar types of information, but they're not identical; they're very different in important ways.

So, I've got a displacement-time graph and a velocity-time graph here, and I'm gonna show you the movement of the same object on both graphs at the same time.

So, in the first stage of movement here, I've got a displacement increasing at irregular amounts, and that indicates a constant velocity.

So, if you look at the velocity-time graph, I've got a constant level of velocity there.

Then I've got this secondary displacement graph where the displacement doesn't change, and that means the velocity is zero.

And as you can see on the velocity-time graph, I've made the line go down to zero, then I'm gonna increase the velocity again, but this time it's a small velocity.

And as you can see on the displacement-time graph, the line goes up again, but this time the gradient of the slope is lower.

So, both graphs show information about movement, but in different ways.

As you saw in those example graphs, the lines, even though they're representing the same movement, don't match each other on the graphs.

If I've got a displacement-time graph that's got a line like this, this indicates that there's a constant velocity.

This object is moving forward at a constant rate, and that on the velocity-time graph would be represented by a line like this.

The velocity is remaining constant at a steady amount, and it's producing a gradual increase in displacement, giving us that straight line.

Now, objects aren't always moving, and a displacement can stay at a constant value.

So, if I've got a displacement here where the object's not changing displacement over the period of time, well that must indicate that the object's not moving; it's got zero velocity.

So, on a velocity-time graph, I'd have a velocity remaining constant at zero.

On those two earlier graphs, we had constant velocities, but velocity's not always constant; objects can accelerate.

So, we can have an object like this.

We've got an increase in velocity, showing that the object is accelerating in a regular way, and that's gonna cause a change in displacement that's going to be greater for every second that passes.

So, on a displacement-time graph, I wouldn't get a straight line at all; I'd get a curve like this.

And as you can see in the first part of the movement, I've got a very shallow gradient.

And later on, the object's moving much faster, and I got a much steeper gradient.

So, increasing velocity produces curves on displacement-time graphs.

Objects can also decelerate, so that would mean that the velocity is decreasing over time.

So, on a velocity-time graph that could be represented with something like this.

A decreasing velocity means the change in displacement every second is gonna get smaller and smaller.

So, I'd end up with a displacement-time graph, something like this.

As you can see at the start, the displacement's increasing quickly, and towards the end of the graph, later on in time, the displacement's flattening out; the gradient is much shallower.

So, a decreasing velocity will give me a curve in that direction.

Okay, let's check if you understood the relationship between these shapes on both types of graph.

I've got a set of movement graphs here, three displacement-time graphs and three velocity-time graphs, and each of them match up.

So, each displacement-time graph has got a matching velocity-time graph, and what I'd like you to do is to match up those pairs.

So, pause the video, match up the three sets of pairs, and then restart, please.

Welcome back.

The first pair we can match up is A and F.

This has got a decrease in velocity, so the displacement is a curve that flattens out.

The second pair we can match is B and D.

And in this one, I've got a constant velocity, and therefore a constant gradient on my displacement-time graph.

And that leaves the third pair as C and E, where the displacement is increasing at a greater rate because the velocity is increasing.

Well done if you got those three.

So far, we've just looked at simple sections of a graph where we've got just one phase of motion, but graphs can show multiple phases of motion.

So, we can have a displacement-time graph like this where I've got a steadily-increasing displacement, and then displacement stops increasing over time.

So, we've got two phases there.

And that would match a velocity-time graph something like this.

So, in the first part of the motion, we've got a constant velocity, and that represents a slope on the displacement-time graph and a flat section of a velocity-time graph.

And then, we've got the velocity falling to zero because the displacement no longer increases.

A graph can show gradual changes in motion as well.

So, I'm going to try and plot a displacement-time graph that shows a constant velocity, and then gradually slow into a stop instead of suddenly stopping; and a velocity-time graph that matches it.

So, here's the first section where we've got some constant velocity which results in that time slope on the displacement-time graph.

And then, I've got a gradual slowing here.

So, that's represented by a curve on the displacement-time graph and a straight line on the velocity-time graph as the velocity gradually falls to zero.

And then, when it reaches zero, I'll put that final section of the velocity-time graph in, and that gives me a displacement that doesn't change.

So, I've got that final section on the displacement-time graph.

So, I've got a complete picture of an object that's moving at steady speed, gradually slowing down to a stop.

Okay, it's time for you to try and interpret a graph that's got several phases of motion.

So, I'd like you to decide which of the lines A, B, C, and D on the displacement-time graph, which is on the right there, matches the motion shown on the velocity-time graph, which is on the left.

So, pause the video, have a think about that, and then restart When you've made your selection.

Welcome back, and the correct answer to that was answer B.

Well done if you selected that.

We've got a velocity that's constant, so that gives us a straight gradient upwards at first.

Then we've got a velocity that decreases, so on the displacement-time graph, we're gonna get a curved section.

And then, in the final bit, we've got another constant velocity, so we're looking for another straight section of the graph, but this time at a shallower gradient because the velocity is less.

So, well done if you selected B.

And now let's check if you can convert the graphs the other way.

So, which line on the velocity-time graph matches the motion shown on the displacement-time graph? You can see there's a displacement-time graph there on the left, and I've got four different lines on the right.

I'd just like you to decide which of those four lines on the right velocity-time graph matches that displacement-time graph.

So, pause the video, make your selection, and restart, please.

Okay, welcome back.

And the correct answer to that was D.

Well done if you selected that.

We can see from the displacement-time graph in the first part of the motion, I've got a steadily increasing displacement, and that indicates a constant velocity.

Then I've got a curved section of the graph, and that indicates that the velocity is decreasing.

And then, I've got a section of the graph where the displacement remains the same, so a zero velocity.

And the only line that matches that was line D.

Well done if you selected that.

And now it's time for the first task of the lesson.

And what I'd like you to do is use everything you've learned so far to sketch a pair of graphs for me.

So, I'd like you to sketch a velocity-time graph that matches the motion shown on the displacement-time graph on the left there.

And I'd like you to sketch a displacement-time graph that matches the motion shown on the velocity-time graph on the right there.

Now, there's no numbers on the graphs; I just want the general shapes.

So, pause the video, sketch your graphs, and then restart, please.

And welcome back.

The velocity-time graph you should have sketched for part one should look something like this.

We've got a constant forwards velocity at first, so constant positive velocity, and that gives us that upward straight slope.

Then we've got a velocity of zero because you can see the displacement doesn't change, so the object's not moving, it's got a velocity of zero.

And then, we gradually curve upwards, and that means a gradual increase in velocity.

That gives us that upwards diagonal line on the velocity time graph.

Well done if you sketched something that shape.

And here's the solution to the second part of that; your graph should look something like this.

At first, we've got a high constant velocity, so we get a straight line going upwards like that on the displacement-time graph.

Then we have a decreasing velocity, so that's a curved section on the displacement-time graph.

And finally, we've got a constant lower velocity.

So, well done if your graph looks something like this.

So, let's move on to the second part of the lesson now, and in it we're going to be converting from one motion graph to another.

So, we'll be reading information from one type of graph, a displacement-time graph, and then using that to construct a velocity-time graph, or the other way around.

So, we're gonna be making those conversions from one graph type to another, and we need to follow fairly standard procedures to do that.

That involves reading data from the first graph, and then we use that data in the speed or the velocity equations.

And finally, from the results of those equations, we can plot the results on the second graph.

So, let's start by looking at a few example graphs to see if we can do that.

So far, we've sketched the graphs to get the general shape, but now we're going to try and take readings from one graph in order to plot the other.

So, I'm going to take readings from a velocity-time graph and plot an accurate displacement-time graph for that motion.

So, here's my velocity-time graph, and I've got three phases of motion here.

I've got a constant velocity of 1.

5 meters-per-second, then stopped; and then a constant velocity of two meters-per-second.

So, what I do is I break the motion down into phases.

In the first phase here, I'm going to calculate the total change in distance, or the increase in displacement, and I can do that using the speed equation.

So, I've got a velocity of 1.

5 meters-per-second, and the object moves for two seconds; that gives me an increase in displacement of three metres.

And I can then plot that on my displacement-time graph.

I've got a constant velocity, so I'm drawing a straight line, and it's got to go up to three metres after two seconds.

So, it gives me that red line section there.

Then I look at the motion between two and five seconds on the velocity-time graph, this section of motion here, and the velocity is zero, so there's gonna be no increase in displacement during two to five seconds.

So, in this section of the graph, I can just draw a straight line like this.

And finally, in the third section of the graph, I've got a velocity of two meters-per-second and a change in time from five to eight seconds.

So, I can calculate the increase in displacement there.

And it's important to note it's the increase in displacement, which is six metres.

So, my displacement's got to go up by another six metres in those final three seconds.

So, I need to increase my displacement from three metres to nine metres to accommodate that.

I've successfully converted our velocity-time graph to a displacement-time graph.

Okay, let's see if you can match up a velocity-time graph to the displacement-time graph that should be produced.

So, which line on the displacement-time graph, which is the graph on the right, shows the same motion as the velocity-time graph on the left there? So, pause the video, make your selection, and restart, please.

Okay, welcome back.

The answer you should have selected was line C.

So, if you look carefully, the velocity is at one meter-per-second there, so after two seconds, the object should have moved two metres.

Then the velocity increases to two meters-per-second, so the gradient would increase on my displacement-time graph and then end up with a total distance after four seconds of six metres.

And that indicates that the red line is the correct one.

Well done if you selected that, So, so far, we've converted velocity-time graphs into displacement-time graphs.

Now we're going to try and do that the other way around, a displacement-time graph into a velocity-time graph.

We follow a very similar procedure, so we break each part of the motion down, and then calculate the velocity for each part.

So, I'm gonna look at my displacement-time graph here and break it into the three sections and find the velocity for each section.

So, in the first section here, I've got a change in displacement of six metres, and a time difference of two seconds, and I can calculate the velocity as three meters-per-second.

So, what I need to do then is translate that, put it onto your other graph, and draw a constant velocity of three meters-per-second at that green line there.

The second part of the motion, well, I've got no change in displacement.

That tells me that I've got a velocity of zero meters-per-second.

So, I can quite simply draw that on the graph here, straight down to zero meters-per-second, and align across for those two seconds there.

And in the third part of the motion, again, I find the change in displacement, and the change in displacement is four metres.

The displacement's gone up by four metres there, and the change in time is four seconds.

So, I can find a velocity of one meter-per-second there, and I can plot that on the graph in the last section here.

And now, I've successfully converted a displacement-time graph into a velocity-time graph.

Let's see if you can match up a displacement-time graph and a velocity-time graph.

So, which line on the displacement-time graph shows the same motion as the velocity-time graph, which is on the right there? So, pause the video, make your selection, and restart, please.

Welcome back.

You should have selected line A there.

So, in the first part of the motion, the first two seconds, I've got a velocity of one meter-per-second, so you would expect the displacement to be two metres after two seconds, which the blue line has.

Then you've got a velocity of zero for another two seconds, so you should have a flat part there, blue dash line, and you do.

And then, we've got another increase in velocity to three meters-per-second, and finally the final section of the line between six and eight seconds, we've got no increase in displacement.

So, that was the blue dash line.

Well done if you got that.

And now, it's time for the second task of the lesson.

And what I'd like you to do is use the techniques I've shown you to draw some accurate graphs.

So, I'd like you to draw an accurate displacement-time graph using the information shown on the velocity-time graph there in red, and then I'd like you to draw an accurate velocity-time graph using the information from the displacement-time graph, which is shown in the greeny-blue there on the right.

So, pause the video, draw your two graphs accurately, and then restart, please.

Welcome back.

And for the first graph, you should have drawn something like this.

We've got zero velocity for the first second, so there's no change in displacement, then we're moving at one meters-per-second for two seconds, so we should get up to two metres after that three second mark.

Then we've got a velocity of three meters-per-second, so that steeper line there.

And finally, back down to a velocity of 0.

5 meters-per-second for the end-two section.

Well done if you got that.

And for the second part of the task, you were asked to draw a velocity-time graph, and you should have come up with a velocity-time graph that looks like this.

Well done if you got that.

And now, it's time to move on to the final part of the lesson, where we're going to be finding information from different motion graphs.

So, we're gonna read values from the graphs and use them in different calculations to find things like distance travelled, velocity, and acceleration.

And we have a displacement-time graph where the motion is only in one direction where the direction of travel doesn't change.

It's quite simple to find total distance travelled.

So, if I've got a graph like this, and as you can see I've got changes in velocity there, but I've not got a change in direction, I've got no decrease in displacement, I can just read off the total distance travelled.

It's the same as the final displacement like this.

So, the distance travelled there would be 10 metres.

This graph, the distance travelled would be 60 kilometres.

So, as long as the direction of travel doesn't change, the displacement and the total distance travelled are the same.

In a lot of motion, we've got direction of travel changing.

But as long as the direction of travel is just along the straight line, so north to south or east to west or something like that, the distance travelled can still be found by just adding the separate phases of motion together.

So, I've got a displacement-time graph here.

We've got displacement kilometres and time in hours, and as you can see, the displacement goes up and then down and then up again.

So, we've got changes of direction here.

And so, to find the total distance travelled, what I have to do is add up all of the changes in displacement.

So, I've got an increase in displacement of 60 kilometres there, and then I travel backwards 40 kilometres, and then forwards again 30 kilometres.

And I can find the total distance travelled just by adding those three together.

So, the distance travelled is those three values, and that gives a total distance travelled of 130 kilometres.

Let's see if you can find a total distance travelled for an object that's moving in two directions.

So, I've got a graph showing the displacement and time for an elevator here.

As you can see, it goes upwards and downwards.

So, what I'd like you to do is find the total distance travelled from its journey where it starts at 50 metres, to the ground, which is at a displacement of zero.

So, pause the video, make your selection from the list on the left, and then restart, please.

Welcome back.

You should have selected 130 metres.

In the first part of the motion, the elevator goes down 20 metres.

In the second part of the motion it goes back up 40 metres, so we've already got 60 metres there, and then down from its maximum height of 70, to the ground, so 70 metres down.

And if we add those three values together, we get a total distance of 130 metres.

Well done if you got that.

When we've got a constant velocity on a velocity-time graph, we can use that to calculate the distance travelled or the increase in displacement.

We can do that as long as we've got a constant velocity, something like this.

So, I've got constant velocity here of six meters-per-second for 40 seconds.

The velocity doesn't change during this motion, and that allows us to use a speed equation.

So, we've got a velocity of six meters-per-second, and we've got a time of 40 seconds.

We can read that off the X-axis there.

And we can use, then, the speed equation to calculate the distance travelled or the final displacement.

So, X, the distance travelled or final displacement, is the velocity, V, times time, T.

And we can take those values from the graph, six meters-per-second for 40 seconds, and that gives us a final distance travelled of 240 metres.

So, this object's moved 240 metres.

Okay, I'd like you to try and calculate distance travelled now.

I've got a lorry; it's got three phases of motion, but I only want you to concentrate on the middle section between two and four hours.

And I want you to work out what distance the lorry travels between two and four hours please.

So, pause the video, make your selection from the list on the left, and then restart, please.

Welcome back.

And the answer to that was 120 kilometres, and we can show the calculation of that here.

And the distance travelled, X, is equal to the velocity times time, V times T.

During that part of the motion, the velocity was 60 kilometres an hour, and it went for two hours; so if we multiply those together, we get 120 kilometres.

Well done if you got that.

When there's a constant acceleration acting on an object, then we can find the acceleration from a velocity-time graph, using the change in velocity and the change in time.

So, I've got a velocity-time graph here, and the object is accelerating between two and four seconds.

You can see the velocity is increasing there.

So, we can find acceleration using the acceleration equation that you may have seen before.

Acceleration is change in velocity divided by change in time.

And in symbols, you might have seen it like this: A equals V minus U over T.

V is the final velocity, and U is the initial velocity, and T is the time.

So, if we look at this section of the graph where the acceleration's happening, we can read off some values and put those into the equation.

The acceleration is five meters-per-second minus two meters-per-second, where V was five meters-per-second, U two meters-per-second.

And T, the change in time, well, that's four seconds to two seconds.

So, we take away two seconds from that four seconds.

We carry out the calculation, and that gives us an answer for the acceleration of 1.

5 meters-per-second squared.

Okay, I'd like you to find out an acceleration for yourself now.

We've got our velocity-time graph here.

As you can see, there's acceleration going on between one and four seconds.

So, I'd like you to find the acceleration between one second and four second for the journey shown.

So, pause the video, calculate the acceleration, and then restart, please.

Welcome back.

You should have selected C for that; 1.

33 meters-per-second squared.

And if we read the values for this section of the graph, the part where it's accelerating as asked, we can substitute the values we read off the graph into the equation, just like that, and that gives us a final answer of 1.

33 meters-per-second squared.

Well done if you got that.

Acceleration isn't always a constant value, and we can see that by a changing gradient on a velocity-time graph.

So, if I've got an object that's got a changing acceleration, I'll end up with a curve on a velocity-time graph like this, and that one there has got the lowest acceleration because the curve isn't changing much; it's gradually increasing.

If I've got a slightly higher acceleration, then I'm going to have a curve that becomes more steep, more rapidly.

So, that dotted black line there would be medium acceleration.

And as you'd expect, if I've got a higher acceleration again, I'm going to get a curve that becomes steeper much more rapidly like that.

Let's see if you can identify the greatest deceleration here.

I've got an object that was moving at six meters-per-second, but which of those lines shows the object that is decelerating of the greatest deceleration? Pause the video, make your selection from the lines below, and then restart, please.

Welcome back.

You should have selected D.

That becoming steepest more quickly, the object is reaching a velocity of zero more rapidly, only takes four seconds.

So, that must have the greatest deceleration.

Well done if you selected that.

And now, it's time for the final task of the lesson.

And this task is explained over the next two slides.

So, the displacement-time graph below shows the motion of a camera drone.

I'd like you to find the total distance travelled between nought seconds and eight seconds, and then I'd like you to find the velocity between five seconds and eight seconds, please.

And the next two parts of the question: this is a velocity-time graph, and it shows the motion of a toy boat.

I'd like you to find the total distance travelled between nought seconds and three seconds, and find the acceleration between six seconds and eight seconds, please.

So, pause the video, answer those four questions, and then restart.

Welcome back.

And the total distance travelled is a sum of these three motions here; we've got 10 metres, 5 metres, and 10 metres, So, the distance is 25 metres.

The velocity between five seconds and eight seconds, we can use readings from the graph and the speed equation to get that, and it gives us 3.

3 meters-per-second.

Well done if got that.

And parts three and four are the total distance travelled between nought and three seconds.

We'll read the velocity, two meters-per-second; it's a constant velocity.

And the time, three seconds.

We can multiply those together to get a distance travelled of six metres.

And the acceleration, for this final part of the graph, we can again read the values for the initial velocity and final velocity, substitute those in and the change in time there, and that gives us an acceleration of minus-one meters-per-second squared.

Well done if you got those.

Okay, we've reached the end of the lesson now, and here's a summary of everything we've learned.

Motion graphs can show the same information in different ways.

So, I've got a displacement-time graph there, and constant velocity is shown by a straight line on that graph.

And changing velocity is shown by a curve.

But in the velocity-time graph, constant velocity is shown by a horizontal line, and constant acceleration is shown by a straight line.

If we've got constant velocity, we can calculate distance travelled using X equals V times T; distance travelled is velocity times time.

If we've got uniform acceleration, we can find the acceleration using A equals V minus U over T; so final velocity minus initial velocity divided by time.

Well done for reaching the end of the lesson.

I'll see you in the next one.