Introduction to Calculus

For a particle moving along a curve $C$ traced by $\boldsymbol{r}(t)$, the derivative of $\boldsymbol{r}(t)$ carries a physical interpretation used throughout this module.

Velocity

$\vec{v}(t)$ is tangent to $C$ and points in the direction of motion.

Speed

Acceleration

$\vec{a}(t)$ measures how the velocity vector changes, both in magnitude (speed) and in direction.