Area Under Velocity Time Graphs | Forces & Motion | Physics | FuseSchool

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You should already know that velocity-time graphs look like this... and how we can use them to map out a journey.

If you’re unsure, you may want to watch this video first...In this video we’re going to look at the area under these graphs and what they represent. Let’s start by looking at a simple velocity-time graph.To find the area underneath the line… Multiply the value on the horizontal axis with the value on the vertical axis.

We are multiplying together the velocity of the object and the time it has travelled for. Look at the unit… 80 metres. The area underneath a graph gives us the total distance that the object has travelled. So, we have velocity, time and distance. The area won’t always be quite so simple to calculate! Velocity-time graphs more commonly look like this…. we can calculate the area underneath the line by cleverly splitting the area into triangles and rectangles.

Remember that the area of a triangle is the base multiplied by its height divided by 2. Can you work out the distance travelled for this velocity time graph? Work out the total area underneath the graph. Pause the video and give it a go.

Did you get it right? 2430 metres?

For most velocity-time graphs, splitting up the area will be relatively obvious... However, you might come across some more complicated plots. Splitting up an area like this will is less obvious.

Whilst it doesn’t matter exactly how you split the area up, the fewer shapes you have, the fewer calculations you will have to do.

As a general tip, try to include a triangle where you see diagonal lines and rectangles where there are horizontal sections. Give this one a go yourself. Pause the video and work out the distance travelled. Did you get it right?

This means that for the journey shown by this velocity-time graph, the object travelled a total distance of 24m.

When doing these calculations just be sure to check the units that you are given because this will affect what unit you will give in your answer for the total distance.

For this one it was seconds and metres per second, so the distance in metres is correct. But for this one… it’s hours and kilometres per hour… so the distance would be measured in kilometres. So, there we have velocity-time graphs… velocity on this axis, time on this axis and the area underneath the graph is the distance. Simple!

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