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The time rate of change of the position of an object

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Instantaneous speed x instantaneous velocity

Related to Distinguish between instantaneous speed and instantaneous velocity I understand that the average velocity is given by the displacement divided by the change in time, and it is a vector quantity … I am also aware that the instantaneous speed is the magnitude of the instantaneous velocity. However, I am unsure how to prove this relationship using the average formulas mentioned above. …
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