Motion as a Curve

Position at each moment

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

• Parametric equations give x and y as functions of a parameter t.
• The same shape can be traced at different speeds and in different directions.
• Eliminate t to find the shape: substitute, or use cos² + sin² = 1.

Steps

1. A point on the move
2. Same circle, different motion
3. Start at the top, go clockwise
4. Crossing the axis
5. Getting rid of the parameter
6. A squashed circle
7. A thrown ball