Idea 4of 6Builds onSame motion, two graphsArea below the line
Area of any shape
Does the area trick hold for any graph?
Today you'll discover
- why strips work whatever the shape
- how a rectangle and a triangle add up
- what to do with area below zero
Think firstThree pieces: steady, stopped, back
Out at 2 m/s for 4 s, stopped, then back for 3 s. Where does it end?
Decide first, then press Next. Watch each piece of the graph become an area.
A velocity–time graph with three flat pieces: above zero, on zero, below zero. After a prediction, the pieces above and below are hatched with their areas. Then a sloping line cut into thin strips. The last step shows a tram's line falling from 10 to 4 and asks how far it went.
See the whole ideathe big idea and the key word, in one place
The big idea
Area adds up any shape. Below zero counts negative.
See the patternRectangle: height × width. Triangle: half of that. A slope is a rectangle under a triangle, or a rectangle at the average height.
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 graph made of several pieces.