<P> For a position vector r that is a function of time t, the time derivatives can be computed with respect to t . These derivatives have common utility in the study of kinematics, control theory, engineering and other sciences . </P> <Dl> <Dt> Velocity </Dt> <Dd> v = d r d t (\ displaystyle (\ mathbf (v)) = (\ frac (\ mathrm (d) (\ mathbf (r))) (\ mathrm (d) t))) </Dd> </Dl> <Dd> v = d r d t (\ displaystyle (\ mathbf (v)) = (\ frac (\ mathrm (d) (\ mathbf (r))) (\ mathrm (d) t))) </Dd> <P> where dr is an infinitesimally small displacement (vector). </P>

Which is a correct position vector r to use