Remark 1

In Kinematics, if the point $\mathbf{f}(t)$ is the position of a moving point in the space $\mathbf{R}^3$ at time $t$, then $\frac{\mathbf{f}(t) - \mathbf{f}(t_0)}{t - t_0}$ is termed the average velocity between the instants $t_0$ and $t$, and its limit $\mathbf{f}'(t_0)$ is the instantaneous velocity (or simply velocity) at the time $t_0$ (when this limit exists).*