Thus, for bodies in pure translation, the velocity and acceleration of every point P in the body are given by: v P = r ˙ ˙ ( t ) = d ˙ ˙ ( t ) = v O , a P = r ¨ ¨ ( t ) = d ¨ ¨ ( t ) = a O , where the dot denotes the derivative with respect to time and v O and a O are the velocity and acceleration, respectively, of the origin of the moving frame M. Recall the coordinate vector p in M is constant, so its derivative is zero.