Position (vector) - Derivatives of Position

Derivatives of Position

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.

Velocity

where dr is an infinitesimally small displacement (vector).

Acceleration

Jerk

These names for the first, second and third derivative of position are commonly used in basic kinematics. By extension, the higher order derivatives can be computed in a similar fashion. Study of these higher order derivatives can improve approximations of the original displacement function. Such higher-order terms are required in order to accurately represent the displacement function as a sum of an infinite series, enabling several analytical techniques in engineering and physics.