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Consider a particle P described by a repetitive chain  \Psi of historically ordered space-time events  \mathsf{\Omega}. Let these events be characterized by their position  \bar{r} and time of occurrence  t. We express this trajectory of P by writing

\Psi \! \left( \bar{r}, t \right)^{\mathsf{P}} = \left( \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2} \, \ldots  \;  \mathsf{\Omega}_{\it{i}} \; \ldots \; \mathsf{\Omega}_{\it{f}} \; \ldots \, \right)

Use these characteristics to calculate a velocity  \overline{\mathsf{v}} for each event \mathsf{\Omega}. Then changes between some arbitrary initial and final events are noted by

\Delta  \overline{\mathsf{v}} = \overline{\mathsf{v}}_{f} - \overline{\mathsf{v}}_{i}

\Delta t = t_{f} - t_{i}

The acceleration vector is defined by the ordered set of three numbers

\overline{a} \equiv   \dfrac{\Delta \overline{\mathsf{v}}}{\Delta t}

This acceleration is used to describe changes in the trajectory of P. It can be experimentally determined by measuring lengths and elapsed times. The norm of the acceleration is written without an overline

a \equiv \left\| \,   \overline{a} \, \right\|

Bidang, Iban people. Sarawak 20th century, 54 x 121 cm. Pilih technique. From the Teo Family collection, Kuching. Photograph by D Dunlop.