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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.
The formula for acceleration is given as a = (v 2 - v 1) / (t 2 - t 1), where a denotes the acceleration, v 2 indicates the final velocity, v 1 represents the initial velocity and t 2 - t 1 is the time interval between the final and initial velocities.