How Fast Right Now

You'll learnhow a slope between two points gives an average speed, and how shrinking the gap between them gives the speed at one instant.

A ball is thrown upward. Between two moments of its flight you can work out an average speed with nothing but a subtraction and a division. But how fast was it going at one exact instant? Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · AVERAGE = A SECANT SLOPE · INSTANT = THE LIMIT OF THOSE AVERAGES · v2

average on [1, 4] = 75 m/s · rate at x = 1 = 90 m/s

Before you start

What you're looking at

The height of a thrown ball, plotted against time. Two moments are marked, at 1 second and at 4 seconds.

The question

How fast was the ball climbing at exactly 1 second, and where does that number come from?

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