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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 final formula for the braking distance is given below. Notice how the acceleration rate is calculated by multiplying the acceleration due to gravity by the sum of the coefficient of friction and grade of the road.