Idea 12of 12Builds onNot a hillHow fast, and which way
Steep means fast
What does a steep line mean?
Today you'll discover
- why the faster walker's line is steeper
- how to measure steepness as metres each second
- how up-or-down says which way
Think firstThink first: which walker is faster?
Steep means fast: as the clock runs, each walker moves along the ground and a dot traces the position–time line behind it; the dot's height is the walker's position at that moment, and the line's steepness is how fast the walker is moving.
Both walk six metres. Amara takes four seconds, Ben takes six. Who is faster?
Decide who is faster before anything is drawn. Then watch, measure, and test it yourself.
Two walkers, Amara and Ben, each on a ground lane with an empty graph beneath them; both walk six metres, in four and six seconds. After a prediction, a player: as the clock runs, both move and each draws a line on the position–time graph, Amara's steeper. Then a shaded triangle under Amara's line reads four seconds across, six metres up, 1.5 metres each second. Then a walk out and back with equally steep rising and falling legs, each triangle carrying its signed rate, plus 1.5 and minus 1.5 metres per second. Then a bench with distance and time sliders and three challenges. Then a recall question, and a cyclist's line climbing twelve metres in three seconds.
See the whole ideathe big idea and the key word, in one place
The big idea
How steep? How fast. Up or down? Which way.
Why it happensRise is a change of position; run is a change of time. Dividing one by the other is exactly what velocity is.
Key word
- slope
- the rise of a line divided by its run; on a position–time graph, the velocity
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?
- Read a velocity off a graph's slope, direction included.