The Road That Was Not on the Graph
Two position–time graphs cross at 3 s. At that instant cars A and B are at the same place, and B is moving three times as fast.
Which feature of the graph tells you the speed?
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Science · Honors Physics
Chapter 1: Kinematics with Calculus Readiness
Gradients and areas say everything the equations do.
Two position–time graphs cross at 3 s. At that instant cars A and B are at the same place, and B is moving three times as fast.
Which feature of the graph tells you the speed?
Make your guess to turn the page.
Still to come: 11 pages · Lab · Words to Know · What We Learned · 4 questions · Explain It in Writing · Open Questions
The idea this lesson is working on — Students read a position–time graph as a picture of the route, so a level road should be flat and a hill should make a hump. The book sets that against the lab, where a car on a level road climbs steadily on the graph, and a car over a hill gives a straight line. Ask: what is on each axis? The idea to reach is slope is a rate, area is a total, and time runs along the bottom.
Graphs work when equations do not — Because slope and area are defined whether or not the acceleration is constant, graphical analysis handles the bike ride and the coffee filter that the kinematic equations cannot. Oresme's treatise is usually dated to the 1350s; the mean speed theorem is associated with William Heytesbury and the Merton College calculators of the 1330s.