Idea 6of 11Builds onThe average sits halfwayStart to finish
The area under the line
How far did the cart go in four seconds?
Today you'll discover
- a shape that grows as the cart covers ground
- why one thin strip is a small piece of distance
- where sixteen metres comes from
Think first2 to 6 m/s in 4 s. How far?
On average 4 m/s, for 4 s. How far did the cart go?
Decide first. Then press play and watch the shaded area grow as the cart moves.
The cart's velocity–time graph with its average drawn across the middle. After a prediction, a player: as the clock runs, the cart moves along a ground line while the dot climbs its line and the region under the line fills with hatching, the ground covered printed inside it. Then one narrow shaded column under the line with its height, width and product printed, and the same small stretch highlighted on a ground line under the graph. Then the whole region cut into sixteen thin strips. Then a dashed box as tall as the average and as wide as the line, with the piece above the average arrowed into the gap below it, labelled 4 metres per second times 4 seconds equals 16 metres east. The last step shows a scooter's graph and asks how far.
See the whole ideathe big idea and the key word, in one place
The big idea
Area adds up the motion: velocity × time = displacement.
Easy to get wrongThe height of the line at the end is 6 m/s, not 16 m. How far is the area, never the height.
Key word
- area
- the region between a velocity–time line and the time axis; its size is the displacement
About this modelBelow the line means moving the other way, not slowing down.
Below the line means moving the other way, not slowing down.
Ready to use it?
- Find a displacement from a velocity–time graph.