  Math Topics

# What Is a Speed Diagram?

Speed diagrams, sometimes called velocity diagrams, are used to describe the correlation between distance, speed and time. In the diagram, we have the time along the first axis ($x$-axis) and the distance along the second axis ($y$-axis). It’s possible to calculate the average speed of different periods of time on the graph. For example, the graph being a horizontal line means there is no movement, because time passes during this period while the distance traveled stays the same. This is how you have to think when you interpret a speed diagram. We will do some calculations based on this diagram below. Before that, let’s have a quick look at the diagram together. The car is not moving from $0.75$ to $1.2$ hours, as marked by the horizontal line. You can also see that the graph is steeper before the break than after the break, which means that the car was driving faster before the break. Due to the break, the average speed for the entire trip is lower than the speed in both the intervals where the car is actually moving.

When a problem talks about a trip that goes somewhere and back again, the graph will still continue to rise. This is because the second axis shows how far we have traveled, not how far we are from our starting point.

Example 1

Look at the speed diagram above and interpret the trip

You can find the total distance they have driven on the second axis. It is $110$ km. To find the average speed, you divide the movement along the second axis (how far they have traveled) by the movement along the first axis (the time they have used). $\begin{array}{llll}\hfill d& =s\cdot t\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill s& =\frac{d}{t}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{110\phantom{\rule{0.17em}{0ex}}\text{km}}{2.25\phantom{\rule{0.17em}{0ex}}\text{h}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \approx 49\phantom{\rule{0.17em}{0ex}}\text{km/h}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

The average speed of the trip, including the break, was $49$ km/h.

You can find the time they used on the trip on the first axis, and it shows you that they used $2.25$ h. That is

which means the drive took $2$ hours and $15$ minutes.

Example 2

Niels Henrik Abel swims out to a reef and back again. He spends $25$ minutes on the trip, which is $500$ meters long in total. He takes a $2$ minute break at the reef before he swims back to shore. Abel swam faster out to the reef than he swam back. Draw a speed diagram that can represent Niels Henrik’s swim. 