A vector-valued function $\mathbf{r}(t) = \langle x(t), y(t) \rangle$ describes the path of a particle in
the plane.
Velocity $\mathbf{v}(t) = \mathbf{r}'(t)$ is tangent to the path.
Acceleration $\mathbf{a}(t) = \mathbf{r}''(t)$ points toward the "turn".
By observing the velocity and acceleration vectors in motion, we gain intuition about how forces shape
trajectories.
Position $\mathbf{r}$
Velocity $\mathbf{v}$
Acceleration $\mathbf{a}$
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