Let's now think of a slightly different concept, the concept of average speed.
So let's say that you decide that on your way from home to school, you decide to stop at a shop, and that shop is halfway between home and school. So it's five hundred metres from your house, and another five hundred metres to school.
So what will that journey look like?
Remember, we said that you're going to do a brisk walk or a light jog, travelling at about one hundred metres per minute, but now we're going to stop at the shop for ten minutes.
Well, you can represent a journey like that on one of these graphs which is called a distance-time graph. So I've drawn the distance on this vertical axis here - distance in metres - and that's a zero all the way up to a thousand metres, home to school. And the time on the horizontal axis and I've labelled this in minutes. I started at zero and I've gone all the way up to twenty minutes.
So this first bit of the journey is the bit of the journey when you're travelling at a hundred metres per minute, jogging along from home to the shop.
So you travel - remember what speed means - you travel one hundred metres in one minute, and two hundred metres in two minutes, and three hundred metres in three minutes, all the way to five hundred metres in five minutes, where the shop is.
You then wait. You stay in the shop for ten minutes, so you don't move. You don't go anywhere. You stay in the same place, but time ticks along. You waste or spend ten minutes in the shop.
Now after ten minutes, you leave the shop and you set off again, travelling at a hundred metres per minute. And what that means, it means that after one more minute, you've gone another hundred metres; in two minutes, two hundred metres; and so on, all the way to the final five hundred metres to school, which takes you five minutes.
So the whole journey, including a stop at the shop, has taken you twenty minutes. And during the whole journey, you have travelled one thousand metres.
So what's your average speed for the journey?
Well, that's the total distance you've travelled, divided by the total time it took. One thousand metres, divided by twenty minutes, that is fifty metres per minute.
In this video Professor Brian Cox introduces the concept of average speed and demonstrates how a distance-time graph can be used to represent a journey and calculate the average speed taken to complete it, using the example of a journey from home to school.
A simple three part distance-time graph is used to show the different phases of a journey and how the speed varies between each phase. The graph is then analysed to estimate the speed at different stages and then the average speed for the whole journey is calculated.
The video demonstrates how a graph can tell a story and give a more complete picture of the journey than just the average speed calculation.
Teacher Notes
Points for discussion:
This video is a good example of the importance of a graph in telling a story.
Students often do not see the point of a graph, but this video demonstrates how a graph can give us more information than just the calculation of average speed.
Suggested activities:
This video could be used once students are familiar with the speed equation and understand what it shows and how to use it.
Alternatively, this video could follow on from clip 3 in this series which introduces speed and how to calculate it.
Following on from this, students could practise interpreting distance-time graphs, starting with talk activities to describe the story behind each graph before calculating average speeds.
The level of difficulty of graphs could be increased. For example, by using more complex axes, using decimals or using points that do not fit neatly onto gridlines.
Students could be asked to calculate the speed at various stages of the journey shown in the graph. The practice of describing and explaining graphs would be beneficial for both KS3 and KS4 students.
Students could then construct their own graph of, for example, a journey of their own and could plot their own measurements of distances and times.
At KS4, this video could be used to revise and reinforce learning about distance-time graphs and how to calculate speed from them before moving on to study velocity-time graphs.
Curriculum Notes
Suitable for KS3, Combined Science and Physics GCSE in England, Wales and Northern Ireland and at National 4 and 5 in Scotland, and Cambridge IGCSE Physics
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An explanation of Hooke’s Law using a spring as an example and showing how overstretching a spring leads to a non-linear relationship between force and extension.
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An introduction to the speed equation, illustrating its logic using the example of a journey from home to school.
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A reminder to always sense-check mathematical answers in physics, using a speed calculation as an example.
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An explanation of the concept of relative speed and how to calculate the relative speeds of two vehicles going in the same direction and in the opposite direction.
