Definition:Instantaneous Acceleration

Definition
Let $B$ be a body in motion.

Let $\Bbb I = \closedint {t_1} {t_2}$ be a time interval.

Let $\mathbf v_1$ and $\mathbf v_2$ be the velocity of $B$ at $t_1$ and $t_2$ respectively.

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

The instantaneous acceleration $\mathbf a$ of $B$ during $\Bbb I$ is defined as the limit of $\overline {\mathbf a}$ as $t_2 \to t_1$:


 * $\mathbf a := \ds \lim_{t_2 \mathop - t_2 \mathop \to 0} \dfrac {\mathbf v_2 - \mathbf v_1} {t_2 - t_2}$

Also see

 * Definition:Acceleration
 * Definition:Average Acceleration