Consider an object travelling with uniform circular motion at speed v moving in a short time-interval δt along the perimeter of a circle radius r. Let the distance moved by the object in that time be δs. If the distance is small, then δs can be considered to be a straight line.By similar triangles δv/v = δs/rSince v = δs/δt then δs can be replaced by vδt. Rearranging gives a = v2/r