Displacement (vector) - Derivatives

Derivatives

For a position vector s that is a function of time t, the derivatives can be computed with respect to t. These derivatives have common utility in the study of kinematics, control theory, and other sciences and engineering disciplines.

Velocity

(where ds is an infinitesimally small displacement)

Acceleration

Jerk

These common names correspond to terminology 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.