Instantaneous acceleration

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

For $\backslash \; vec\; \{v\}\; (t\_1)$ speed at the moment $t\_1$ and $\backslash \; vec\; \{v\}\; (t\_2)$ speed at the moment $t\_2$, one has that the instantaneous acceleration is the limiting of the difference speeds $\backslash \; vec\; \{v\}\; (t\_1)$ and $\backslash \; vec\; \{v\}\; (t\_2)$ when the time interval $\backslash \; Delta\; T\; =\; t\_2\; -\; t\_1$ tends towards zero:

$\backslash \; vec\; \{has\}\; =\; \backslash \; lim\_\; \{\backslash \; Delta\; T\; \backslash \; to\; 0\}\; \backslash \; frac\; \{\backslash \; vec\; \{v\}\; (t\_2)\; -\; \backslash \; vec\; \{v\}\; (t\_1)\}\{\backslash \; Delta\; T\}\; =\; \backslash \; frac\; \{\backslash \; textrm\; \{D\}\; \backslash \; vec\; \{v\}\}\; \{\backslash \; textrm\; \{D\}\; T\}\; =\; \backslash \; frac\; \{\backslash \; textrm\; \{D\}\; ^2\; \backslash \; vec\; \{X\}\}\; \{\backslash \; textrm\; \{D\}\; t^2\}$

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

See too

• Speed

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