Calculus › Section M · Vector-valued functions › Topic M.3
Velocity and acceleration
A position vector that depends on time describes a journey, and calculus turns that journey into physics: one derivative gives the velocity vector, a second gives the acceleration, and for projectiles two integrations recover the whole flight path from nothing but gravity.
In this topic
- Why motion needs vectors
- Velocity, acceleration, speed
- Worked example: a plane curve
- Worked example: a space curve
- From acceleration back to position
- Projectiles: the model and its assumptions
- Worked example: clearing the wall
- Applied: constant speed, real acceleration
- Common mistakes to avoid
- Key takeaways
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Standards: 9 (BC)