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Deriving the centripetal acceleration formula. A body that moves in a circular motion (of radius r) at constant speed (v) is always being accelerated. The acceleration is at right angles to the direction of motion (towards the center of the circle) and of magnitude v2 / r. The direction of acceleration is deduced by symmetry arguments.
When the acceleration is constant, Both average acceleration and instantaneous acceleration are constant and equal so we can write the formula of constant acceleration and instantaneous acceleration as: where, is the velocity at and is velocity at later time.