Idea 2of 6Builds onTwo readings of any graph
Curved means changing
What does a curved line mean?
Today you'll discover
- why a steady walk is a straight line
- what a curve says about the speed
- how to read 'speeding up' without numbers
Think firstA position–time line that curves upward
This line gets steeper as time passes. What is the cart doing?
Decide first, then press Next. Compare the curve with a straight line.
A position–time line that curves upward, getting steeper. After a prediction, a straight line for Amara's steady walk is shown for comparison, then a straight line touching the curve at one point whose steepness is the speed at that instant, then the curve again with its meaning named. The last step asks what a line bending toward flat means.
See the whole ideathe big idea and the key word, in one place
The big idea
Straight: steady speed. Curved: the speed is changing.
Easy to get wrongA curve on a position–time graph is not a bend in the road. It is the speed changing.
Key word
- non-uniform motion
- motion whose velocity is changing: a curve on a position–time graph, a sloping line on a velocity–time graph
About this modelThe line is not the path. Up means further east, not uphill; a falling line means walking back, not walking downhill.
The line is not the path. Up means further east, not uphill; a falling line means walking back, not walking downhill.
Ready to use it?
- Tell speeding up from slowing down on a curved line.