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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.
a=dv/dt. By definition, acceleration is the rate of change of velocity. In mathematical notation, it is given as the formula stated above. Two special cases: 1. When acceleration is constant: The rate of change is a constant. Therefore, it can be calculated by: a=(vf - vi) / t where a is acceleration vf is final velocity vi is initial velocity and t is time taken 2. When velocity is constant: Velocity is not changing. The rate of change of velocity is zero.