Editing Position (geometry) (section)

==Derivatives==
{{see also|Displacement (geometry)#Derivatives}}
[[File:Kinematics.svg|thumb|Kinematic quantities of a classical particle: mass&nbsp;''m'', position&nbsp;'''r''', velocity&nbsp;'''v''', acceleration&nbsp;'''a''']]

For a position vector '''r''' that is a function of time ''t'', the [[time derivative]]s can be computed with respect to ''t''. These derivatives have common utility in the study of [[kinematics]], [[control theory]], [[engineering]] and other sciences.

;[[Velocity]]
:<math>\mathbf{v} = \frac{\mathrm{d}\mathbf{r}}{\mathrm{d}t},</math>
:where d'''r''' is an [[Differential (infinitesimal)|infinitesimally]] small [[displacement (vector)]].
;[[Acceleration]]
:<math>\mathbf{a} = \frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} = \frac{\mathrm{d}^2\mathbf{r}}{\mathrm{d}t^2}.</math>
;[[Jerk (physics)|Jerk]]
:<math>\mathbf{j} = \frac{\mathrm{d}\mathbf{a}}{\mathrm{d}t} = \frac{\mathrm{d}^2\mathbf{v}}{\mathrm{d}t^2} = \frac{\mathrm{d}^3\mathbf{r}}{\mathrm{d}t^3}.</math>

These names for the first, second and third derivative of position are commonly used in basic kinematics.<ref name='stewart'>{{cite book
|last= Stewart
|first= James
|author-link=James Stewart (mathematician)
|title= [[Calculus]]
|publisher= Brooks/Cole
|year= 2001
|edition= 2nd
|isbn= 0-534-37718-1
|chapter= §2.8. The Derivative As A Function
}}
</ref> 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 [[Taylor series|a sum of an infinite sequence]], enabling several analytical techniques in engineering and physics.