Definition:Instantaneous/Velocity

Definition

Let $B$ be a body in motion.

Let $\Bbb I = \closedint t {t + h}$ be a time interval.

Let $\mathbf s_1$ and $\mathbf s_2$ be the displacement of $B$ at $t$ and $t + h$ respectively.

Let $\overline {\mathbf v}$ denote the average velocity of $B$ over $\Bbb I$.

The instantaneous velocity $\mathbf v$ of $B$ at time $t$ is defined as the limit of $\overline {\mathbf v}$ as $h \to 0$:

$\mathbf v := \ds \lim_{h \mathop \to 0} \dfrac {\mathbf s_2 - \mathbf s_1} h$

Also see

• Definition:Velocity
• Definition:Average Velocity

• Definition:Instantaneous Acceleration

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): instantaneous
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): instantaneous