One Rate You Measured, and One Rate You Want

You'll learnto write every moving quantity as a function of time, apply d/dt so each one picks up its own rate factor, and use the shape of a problem to remove a rate you were never given.

An oil slick spreads in a circle. Its radius grows at a steady rate, and yet its area races away faster and faster. One measured rate, one wanted rate, and a chain rule between them. Eleven short steps; press Next for each one.

11 STEPS · 6 QUICK CHECKS · EVERY MOVING LETTER GETS A RATE FACTOR · A CONSTRAINT REMOVES THE RATE YOU DO NOT HAVE · v2

A(t) = π [ r(t) ]² ⇒ dA/dt = 2π r · dr/dt · one measured rate drives another

Before you start

What you're looking at

An oil slick spreading in a circle. Its radius grows at a steady half meter per second, which is the one rate anybody measured.

The question

The radius rate never changes, so why does the area rate keep climbing?

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