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The question is too vague for a proper answer.
Distance can crop up in the context of speed, acceleration, kinetics, etc. In each case the definition and formula may vary.
There is also the concept of distance between two points in a metric space and the measure of distance will depend on the metric defined on the space. The Euclidean (or Pythagorean) metric and the Minkovsky (or taxicab) metric are two of the more common metrics but there are loads more.
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