Let \(I\subset \mathbb R\) be a time interval, \(\mathbb R^n\) (e.g. for \(n=3\)) be the \(n\)-dimensional real vector space and let \(x:I\to \mathbb R^n\) by trajectory function of some object in this space, which is differentiable at a given point in time \(t\in I\). Then the derivative \[v(t):=\operatorname {lim} _{h\rightarrow 0}\,{\frac {x(t+h)-x(t)}{h}}=\dot x(t)\] is called the instantaneous velocity of the object at the time \(t\).
