Lesson video

Hello there.

My name's Mr. Forbes and welcome to this lesson from the Measuring and Calculating Motion Unit.

In this lesson we're going to be taking a detailed look at velocity-time graphs and how we can take readings from them to find out the velocity at certain times and how we can use them in different calculations such as calculating acceleration.

By the end of this lesson, you're going to be able to describe velocity-time graphs, be able to take values from those graphs in order to identify velocity at certain times, and also to be able to calculate acceleration for different parts of the motion.

These are the keywords you'll need to understand to get the most of the lesson.

The first is displacement-time graph, and a displacement-time graph shows the displacement of an object over a period of time.

And remember the displacement is how far an object is from its starting point in a particular direction.

A velocity-time graph shows how the velocity varies over time.

Acceleration means a change in velocity, so acceleration is the rate of change of velocity, and deceleration is used to describe an object that is slowing down where its velocity is decreasing over time.

And here are those keywords again with the descriptions.

You can return to this slide at any point during the lesson.

This lesson's in three parts, and in the first part we're going to be looking at the structure of a velocity-time graph and how it's different than a displacement-time graph.

We're also going to be taking some readings from those graphs to find velocities at certain times.

In the second part of the lesson, we are going to be trying to find the acceleration based upon the data in the graph.

And in the third part of the lesson, you are going to be sketching some velocity-time graphs based upon descriptions of motion.

So when you're ready, we'll start with looking at velocity-time graphs.

Okay, let's start this lesson by looking at a displacement-time graph, which is something you should have seen before.

A displacement-time graph shows the displacement of an object over a period of time and the displacement is how far that object is from a starting point.

So we can have a graph like this showing the movement of an object.

And as you can see, displacement changes over time.

The displacement is shown on the y-axis here, and it's usually measured in things like metres, but it could be measured in other distance units and the time is shown on the bottom axis here.

In this graph you can see in the first five seconds displacement increasing, so the object's moving away.

Then in the next 10 seconds, the object's displacement isn't changing, so we have a constant position, and in the final 15 seconds the object is moving away again.

This time the displacement's not going up as fast, so it's going a bit slower.

And here's a velocity-time graph and straight away you can see it looks very similar to a displacement-time graph, but this graph is showing how the velocity changes over time, not the displacement.

So even though it looks similar, it gives different information.

So time again is shown along the bottom axis, the x-axis the, but this time the velocity is shown on the y-axis.

So in the first 20 seconds here, you can see the velocity is increasing.

Then in the next 20 seconds the velocity is constant and then the velocity is increasing again for the five to 20 seconds.

As I've said, velocity-time graphs and displacement-time graphs may look very similar, but they show different information.

So we've got a displacement-time graph here and a velocity-time graph here.

This one shows displacement.

This one shows velocity.

It's important to check those those axes very carefully so you know what type of graph you're trying to analyse to find information from because they show very different information, as we'll see during this lesson.

Okay, it's time for the first check now, and what I'd like you to do is to identify which two of these graphs are velocity-time graphs please.

So pause the video, check the graphs carefully, select the correct two, and then restart please.

Okay, welcome back.

And you should have selected graph a and graph c.

And the reason for that is, well, we can examine the y-axis here, and in the first one for graph a, it says velocity and gives a unit of metres per second.

So that's obviously a velocity-time graph, graph b, that's got displacement, so that's not, and graph c, although it just has a letter, the y, it's got a unit of kilometres per hour and kilometres per hour is a velocity or a speed.

So that must be a velocity-time graph.

Well done if you selected those two.

Well the first thing we can do with a velocity-time graph is find the velocity at any particular moment.

So I've got a graph here that shows the movement of a bicycle and as you can see, the velocity is shown on the y-axis there going from nought to six metres per second and the time's across the bottom there on the x-axis.

So if we wanted to find out the velocity of the bicycle at time equals 20 seconds, what we do is find 20 seconds on the axis and then look upwards until we find the line of motion.

And then we could look across and read off the velocity and it's two metres per second there.

If you wanted to do the same thing at 35 seconds, we could look up and then across and find the bicycles moving at four metres per second there.

And we can do the opposite as well.

We can find a time for a certain velocity.

So when does the bicycle reach five metres per second? Well, we find five metres per second on the y-axis and then we look downwards.

We find it's 40 seconds, so it took 40 seconds to reach five metres per second.

So let's check that You can read values off the graph.

I've got velocity-time graph here for a lorry and I'd like to know what's the velocity of the lorry at time equals 20 minutes? So pause the video, find that, and then restart please.

Okay, welcome back and hopefully you selected 35 kilometres an hour.

If you look up from the time 20 minutes to find the line and then across, you'll find it's halfway between 30 and 40, the 35 kilometres per hour.

Well done if you've got that.

The slope or gradient on a velocity-time graph shows when the velocity is changing.

So I've got a velocity-time graph here with changing velocity in three different sections.

So if we look at the first section here, you can see that the velocity is increasing during those first 20 seconds.

So from naught to 20 seconds, we've got an increase in velocity and we can say that the object is accelerating.

Accelerating meaning an increase in velocity there.

In this second section of the graph, these 20 seconds, you can see that the velocity isn't changing, it's constant at four metres per second throughout that.

So the object isn't accelerating at all.

There's a constant velocity between 20 and 40 seconds.

And in the final section of the graph you can see the velocity here is decreasing.

So there's a decrease in velocity and we can describe that as decelerating.

The object is decelerating or slowing down.

I've got a graph here and it's in four sections, a, b, c, and d.

And I'd like you to decide whether the remote control car is accelerating, decelerating, or moving at content velocity for each phase of motion.

So pause the video, make your decision for each, and then restart please.

And welcome back.

For section a, you can see though that the velocity is not changing for that first section of motion.

So we've got constant velocity there.

In section b, you should see that the velocity is increasing, so that's an acceleration.

Section c, again, the velocity is constant, so constant velocity.

And for section d, the velocity's decreasing.

So that's decelerating.

So well done if you've got that.

So far we've only seen velocity-time graphs that show positive velocity, but the graphs can show positive and negative velocity as well.

So here we've got that movement of a goods train, a really large train, and it's got positive and negative velocity shown on the graph.

So this positive velocity will indicate direction in one motion, and then this section at the bottom will indicate motion in the opposite direction.

Those directions might be anything such as north and south, but they could be, if it this was a different object, it might be up and down, or it could be left and right, but it just shows opposite motion in the top half and the bottom half of this graph.

Okay, another check of your understanding of motion on a velocity-time graph.

This one includes positive and negative velocities.

I'd like you to describe how the motion of this elevator can be described between t equals 10 seconds and t equals 15 seconds.

Choose two of the options on the left there, moving upwards, moving downwards, speed decreasing, and speed increasing.

So pause the video, make your two selections, and then restart please.

Welcome back.

You should have chosen moving upwards and speed decreasing.

If you look carefully at the highlighted section, you can see the velocity is positive in that section.

So that means that it's moving upwards, even though the slope is downwards and the speed is decreasing because the velocity is decreasing during that section as well.

Well done if you've got those two.

Okay, it's time for the first task of the lesson here and I've got motion showing three remote control cars in an eight second long race.

And what I'd like you to do is to identify which car stops at the end of the race, identify which car reached the highest velocity and when that happened, state the velocity for each of the three cars at time equals four seconds, and describe the movement of just car b between two seconds and five seconds.

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

Okay, welcome back.

And first of all, let's identify the car which stops.

Well, that's car c.

Its velocity is zero in the race.

The other two cars, a and b, are still moving.

Identify which cars reached the highest velocity and when.

Well, we can see that the highest points, that blue line there, that's car b, and it reached the highest velocity at that point, which is 1.

5 seconds.

State the velocity of each car time equals four seconds.

Well we have to look carefully up from the four seconds mark here and we should be able to see that car a is going at one metres per second, and so is car b, and car c is travelling at 1.

5 metres per second.

Well done if you've got those three.

And the final part of the task was to describe the movement of car b between two seconds and five seconds.

And as you can see, car b is decreasing its velocity, it's gone down by 1.

5 metres per second during a period of three seconds.

So well done if you identified that information.

Okay, it's time for the second part of the lesson now, and in it we're going to be using velocity-time graphs to find acceleration.

Let's start this part of the lesson with a look at the acceleration equation that you should already be familiar with.

So the acceleration of an object is the rate of change of velocity and that means how much the velocity is changing every second.

So an acceleration of four metres per second would mean that the object's velocity is changing by four metres every second.

Acceleration can be calculated using this equation.

Acceleration is change in velocity divided by time taken, or written in symbols, a equals delta v over t, where a is the acceleration and that's measured in metres per second squared.

The change in velocity is represented by delta v and that's measured in metres per second, and the time is measured in seconds, t.

To calculate acceleration then, we need the initial velocity and the final velocity in order to calculate change in velocity and both of those can be read from a velocity-time graph and we can use that then to calculate the average acceleration for a section of motion.

So I've got a simple velocity-time graph here and we're going to try and find the acceleration during the first five seconds.

And to do that we identify the initial velocity and that's zero metres per second there at the bottom and then the final velocity after those five seconds and that's four metres per second.

And we can then get a change in velocity, which is four metres per second, the difference between those two values.

Then we can substitute into the equation for acceleration and that gives us a calculation like this.

We do the sums and that gives us an acceleration of 0.

8 metres per second squared for that five seconds of motion.

To check if you can do that, I'd like you to find the average acceleration during the first eight seconds of this ball that's rolling across a desk.

So you can see I've got a graph there.

What I'd like you to do is to calculate the acceleration during those first eight seconds please.

So pause the video, do your calculation, and then restart.

Welcome back.

Well, we write out the initial velocity and final velocity by identifying those two points on the graph there, got an initial velocity of zero, final velocity of four, so I've got a change in velocity of delta v of four metres per second.

Then I substitute it into the equation putting in the value for delta v and the change in time and that gives me an acceleration of 0.

5 metres per second squared.

Well done if you got that.

It's important to realise that we need to use the change in velocity to calculate acceleration, not an absolute value.

So looking at this graph, we can see there's several different key velocities there.

Starts at one metres per second, goes up to five metres per second, and then back down to two metres per second.

And if I want to work out the acceleration for the last part of the graph from six to 10 seconds, then I need to make sure I use the change in velocity.

So I identify the initial velocity five metres per seconder and then the final velocity, which is much less, it's two metres per second.

So this object's slowing down and then I've got a change in velocity of minus three metres per second and then I can substitute that value into my calculation using the change in velocity and the change in time.

That's minus three metres per second divided by four seconds and that gives me an acceleration of minus 0.

75 metres per second squared.

Okay, it's time for you to try and find an acceleration.

I'd like you to find the average acceleration between two seconds and seven seconds for this rolling ball.

So I'll take the information for the graph and calculate the average acceleration please.

Pause the video, do that calculation, and then restart.

Welcome back.

And what you should have done is identify the initial velocity and the final velocity and that gives you a change in velocity of three metres per second.

And then you substitute that into the equation.

Putting in the change in time as well from two to seven seconds is a five second interval and that gives an acceleration of 0.

6 metres per second squared.

Well done if you've got that.

When I've got motion that only involves constant accelerations, I can find the instantaneous acceleration at any point by looking at the gradient of the straight line sections of the graph.

So in this section of the graph, a straight line, I've got constant acceleration and so the instantaneous acceleration is the gradient of that line, and as you can see, there's a four seconds and a change in velocity of four metres per second.

That gives us an acceleration of one metres per second squared for any point along that section of the line.

Between four and six seconds, there's no change in velocity, so there's no acceleration.

Then I can look at the instantaneous acceleration of this section of the graph and I find it's 0.

, sorry, it's minus 0.

5 metres per second squared between six and 10 seconds.

So for example, at eight seconds, the instantaneous acceleration is minus 0.

5 metres per second squared.

Okay, I'd like you to find an instantaneous acceleration for me using that technique.

I'd like to know what's the instantaneous acceleration for this object at time equals five seconds? So pause the video, work out the acceleration, and then restart please.

Okay, welcome back.

You should have found the instantaneous acceleration is minus 0.

75 metres per second squared.

If we look at the gradient of this section, we've got a time of four seconds and we've got a change in velocity of minus three metres per second.

So we'll get the acceleration by finding the change in velocity divided by the change in time.

And that gives me minus 0.

75 metres per second squared.

Well done if you got that.

Acceleration isn't always constant and so we end up with graphs that aren't just made up of straight lines.

So changing acceleration is shown by a changing gradient and that gives us a curve on a graph.

So in this graph we've got velocity and time and the velocity is not changing uniformly, the acceleration is not constant.

The steeper the gradient, the greater the acceleration is.

So in this first few seconds of the graph we've got high acceleration because we've got steep gradient.

And then towards the end of the graph, we've got lower acceleration because the gradient is lower there.

So the gradient indicates the acceleration.

And let's see if you understand the relationship between gradient and acceleration.

At which point is the acceleration greatest for this drone? Is it point a, b, c, or d? So pause the video, make your selection, and restart please welcome back.

You should have selected c.

That's where the gradient of this curve is steepest.

So the acceleration is greatest there.

Well done if you've got that.

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

I've got a graph here showing the motion of a robot that works in a warehouse moving things around and I'd like you to look carefully at that graph.

I'd like you to then state the velocity of the robot at time equals 15 seconds.

Describe the movement of the robot between 40 seconds and 60 seconds.

Identify when the robot has the greatest acceleration, and finally find the acceleration of the robot between 20 and 30 seconds.

So pause the video, work out your answers to that, and restart please.

Welcome back.

Well, to state the velocity of the robot at time 15 seconds, we look carefully at the graph, find 15 seconds and look across and find the velocity is two metres per second.

Describe the movement of the robot between 40 seconds and 60 seconds.

Well, the robot was decelerating.

You can see the velocity going down there from five metres per second to nought metres per second, and identify when the robot has the highest acceleration.

Well, we look for the steepest gradient, and that's between 20 seconds and 30 seconds.

Well done if you've got those three.

And now we've asked to find the acceleration of the robot between 20 and 30 seconds.

So we look at the values from the graph, identifying the initial and final velocity, finding the change in velocity and the change in time there.

We substitute those into the equation and that should have given you an acceleration of 0.

3 metres per second squared.

Well done if you got that one.

Now it's time to move on to the final part of the lesson.

And in it we're going to look at how to use information to plot velocity-time graphs of our own.

Now we're often given tables of data and asked to plot graphs from that, but sometimes we can be given written information and we have to use that information to plot the graph instead.

And we're gonna go through the process of plotting or sketching a graph based on written information.

To sketch a graph, we need to read the information very carefully, because we are going to have to find the maximum and minimum on the scales we need to plot the graph.

The maximum and minimum velocity is gonna be needed so we can get a suitable scale on the y-axis.

And so is the total time for the journey.

We need to find that so that we know the maximum time.

So we're gonna read through a few passages and try and identify those.

So we're going to try and identify the highest velocity needed on our velocity-axis for a graph for quite a bit of information.

And I've got the information in the box there.

So we've got a jogger is travelling at constant velocity of 3.

5 metres per second for 60 seconds along a straight road.

They see a friend ahead and accelerate up to 4.

2 metres per second in four seconds.

So they picked up the speed there, and they continue running at that speed for 30 seconds.

When they get closer, they realise they was mistaken and they pick up the speed to 5.

2 metres per second in five seconds to get past quickly.

After they're passed, they slow down to three metres per second for 60 seconds to catch their breath a little.

So there's quite a lot of information there.

I'd like you to read through it again and then decide on what maximum value you would use on velocity-axis please.

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

Okay, welcome back.

Hopefully you selected six metres per second, and the reason to do that is we look through all information and find the maximum speed or velocity, and that was 5.

2 metres per second, but we have to make our graph slightly larger than that to make sure it all fits on.

If we had chosen three or four metres per second, they'd have both been too small and 10 metres per second.

Well, that's far too large.

So six metres per second was the best choice for the velocity-axis.

Well done if you chose that one.

And then we've gotta choose a best value for the time axis.

So I've got another journey described here and I'd like you to decide what would be the best final value for the time axis for this information.

So a stationary car accelerates to a velocity of 15 metres per second in 20 seconds.

It then travels for 30 seconds at a constant velocity.

The driver sees a hazard head and comes to a stop in eight seconds.

They wait 22 seconds before they accelerate back up to 30 metres per second, taking 10 seconds to do so.

So pause the video, decide how long the time axis would need to be to fit that entire journey on, and then restart please.

Welcome back.

Hopefully you selected 90 seconds as the the best value for it.

If we look through the information, we've got 20 seconds for first part of motion, and then in 30 seconds, then an eight second part, then a 22 second part, and then a 10 second part.

Adding all all those together gives us a total time of 90 seconds.

So my graph should go up to 90 seconds to fit all of that motion in.

Well then if you selected that.

Once we've decided on our scales by reading the information, we need to plot the information one stage at a time.

So I've got some information here and we're gonna go through it each stage and plot the part of the graph that it relates to.

So we can start off with the first phase.

We've got a stationary car, so we're gonna be starting at zero, zero here and it accelerates to a velocity of 15 metres per second in 20 seconds.

So I need to draw a nice straight line, and it's accelerated to 15 metres per second.

So it ends at 15 metres per second there, and it takes up 20 seconds.

The next phase of the motion is it then travels for 30 seconds at that constant velocity.

So we'll go across 30 seconds and the velocity doesn't change.

So we get a flat section of the graph there.

Then the driver's seeing a hazard and comes to a stop in eight seconds.

So we have this section of the graph where it goes down very steeply and it takes eight seconds to go all the way down to zero metres per second 'cause it's come to a stop.

Then we've got a weight of 22 seconds, so we can draw that on.

They're not moving, so the velocity is zero for 22 seconds.

We draw this section and then they accelerate back up to 13 metres per second, taking 10 seconds to do so.

So the velocity's gonna go back up to 13 metres per second there.

And that's all the information translated to a graph.

So you saw we draw each section of the motion or each phase of the motion separately.

So I'd like you to read through this information and decide how many separate phases of motion or how many lines you're gonna need to draw on the graph.

So pause the video, read through carefully, make your selection, and then restart.

Welcome back.

You should have selected those five.

And the easiest way to identify that is to look at how many different sections of timing there are.

And if we circle them here you can see there are five different time values given there.

So five different phases of motion.

Well done if you spotted that.

Now it's time for you to try and plot a graph using information.

So I've got information in the box here about car journey and I'd like you to draw a velocity-time graph based upon this journey.

A car is travelling at a steady speed of 10 metres per second along a straight road for 10 seconds.

The driver then sees a traffic light and brings the car to a complete stop in five seconds.

After waiting 15 seconds for the light to change, he accelerates to 15 metres per second, taking 10 seconds to do that.

They then stay at constant speed for 15 more seconds before moving onto a faster road where the driver accelerates to 20 metres per second in 15 seconds.

So pause the video, use that information to plot a graph, and then restart please.

Welcome back.

Hopefully your graph looks something like this.

We've got six separate phases of motion, so well done if you completed that.

Okay, we've reached the end of the lesson now and here's a summary of the information you should have learned during it.

Our velocity-time graph shows changes in velocity over a period of time and you can see I've drawn velocity-time graph here with a couple of different lines on it.

The acceleration is the gradient of the line on the graph, and so you can see constant velocities shown by a flat line there.

Constant acceleration is shown by a gradient slop upwards and constant deceleration, a straight line sloping downwards.

We can have curves on there as well, showing changing accelerations.

So I've got a blue curve though with high acceleration at the start and lower acceleration at the end.

And as I mentioned, deceleration is shown by a negative gradient.

Well done for reaching the end of the lesson.

I'll see you in the next one.