# Instantaneous acceleration

The instantaneous acceleration is the temporal derivative speed (second derived from the position) at one moment T given.

For $\ vec \left\{v\right\} \left(t_1\right)$ speed at the moment $t_1$ and $\ vec \left\{v\right\} \left(t_2\right)$ speed at the moment $t_2$, one has that the instantaneous acceleration is the limiting of the difference speeds $\ vec \left\{v\right\} \left(t_1\right)$ and $\ vec \left\{v\right\} \left(t_2\right)$ when the time interval $\ Delta T = t_2 - t_1$ tends towards zero:

$\ vec \left\{has\right\} = \ lim_ \left\{\ Delta T \ to 0\right\} \ frac \left\{\ vec \left\{v\right\} \left(t_2\right) - \ vec \left\{v\right\} \left(t_1\right)\right\}\left\{\ Delta T\right\} = \ frac \left\{\ textrm \left\{D\right\} \ vec \left\{v\right\}\right\} \left\{\ textrm \left\{D\right\} T\right\} = \ frac \left\{\ textrm \left\{D\right\} ^2 \ vec \left\{X\right\}\right\} \left\{\ textrm \left\{D\right\} t^2\right\}$

The instantaneous acceleration is represented by a vector and is measured in meters a second square m·s-2.

## See too

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