Definition:Instantaneous/Acceleration
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Definition
Let $\Bbb I = \closedint t {t + h}$ be a time interval.
Let $\mathbf v_1$ and $\mathbf v_2$ be the velocity of $B$ at $t$ and $t + h$ respectively.
Let $\overline {\mathbf a}$ denote the average acceleration of $B$ over $\Bbb I$.
The instantaneous acceleration $\mathbf a$ of $B$ at time $t$ is defined as the limit of $\overline {\mathbf a}$ as $h \to 0$:
- $\mathbf a := \ds \lim_{h \mathop \to 0} \dfrac {\mathbf v_2 - \mathbf v_1} h$
Also see
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): acceleration
- 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): acceleration
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): instantaneous