Editing Position (geometry) (section)

===Mechanics===

{{main|Newtonian mechanics|Analytical mechanics|Equation of motion}}

In any [[equation of motion]], the position vector '''r'''(''t'') is usually the most sought-after quantity because this function defines the motion of a particle (i.e. a [[point mass]]) – its location relative to a given coordinate system at some time ''t''.

To define motion in terms of position, each coordinate may be parametrized by time; since each successive value of time corresponds to a sequence of successive spatial locations given by the coordinates, the [[continuum limit]] of many successive locations is a path the particle traces.

In the case of one dimension, the position has only one component, so it effectively degenerates to a scalar coordinate. It could be, say, a vector in the ''x'' direction, or the radial ''r'' direction. Equivalent notations include

:<math> \mathbf{x} \equiv x \equiv x(t), \quad r \equiv r(t), \quad s \equiv s(t).</math>