Speed at an Instant

Secants shrink into tangents

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The average rate of change is the slope of a secant line.
• Shrinking the interval turns secants into the tangent line: the instantaneous rate.
• For $d = t^2$, the speed at time $t$ comes out as $2t$.

Steps

1. Average speed
2. Right now
3. Shrink the interval
4. Why it approaches 2
5. Zoom until it’s straight
6. At t = 3
7. Find the flat spot