From the kinematics of curved motion it is known that an object moving at tangential speed v along a path with radius of curvature r accelerates toward the center of curvature at a rate a c = lim Δ Δ t → → 0 Δ Δ v Δ Δ t , a c = v 2 r Here, a c is the centripetal acceleration and Δ Δ v is the difference between the velocity vectors at t + Δ Δ t and t .