Calculus of Motion

Velocity and acceleration as derivatives

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Velocity is the derivative of position, and acceleration is the derivative of velocity.
• At the top of a throw, $v = h'(t) = 0$.
• The constant-acceleration equations follow directly from differentiating.

Steps

1. Connect the ideas
2. Position, velocity, acceleration
3. Velocity at a moment
4. Acceleration
5. Where the motion equations come from
6. When does it stop?