Two Rates, and the Slope They Make Together

You'll learnto tell the two motion rates apart from the slope of the path.

A point on a path has two speeds at once: how fast x changes with time, and how fast y changes with time. Divide each by time and you get its motion; divide one by the other and you get the slope of the path itself. Three rates share the stage, and only one of them is the tangent.

8 STEPS · 6 QUICK CHECKS · START · DIRECTION · EXTENT · v2

Unit 4 is not assessed on the AP exam; schools include it where local requirements ask.

arrowheads show the direction of travel

Before you start

What you're looking at

Δx, Δy, and Δt shown separately, before any of them are combined.

The question

How fast is x changing per unit time, y per unit time — and y per unit of x?

Watch for

Δx/Δt and Δy/Δt (the motion rates) revealed before Δy/Δx (the path's slope), each with its own units.

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