Editing Displacement (geometry) (section)

== Derivatives ==
{{see also|Position (geometry)#Derivatives}}

For a position vector <math>\mathbf{s}</math> that is a function of time <math>t</math>, the derivatives can be computed with respect to <math>t</math>.  The first two derivatives are frequently encountered in physics.

;[[Velocity]]
:<math>\mathbf{v} = \frac{d\mathbf{s}}{dt}</math> 
;[[Acceleration]]
:<math>\mathbf{a} = \frac{d\mathbf{v}}{dt} = \frac{d^2\mathbf{s}}{dt^2}</math>
;[[Jerk (physics)|Jerk]]
:<math>\mathbf{j} = \frac{d\mathbf{a}}{dt} = \frac{d^2\mathbf{v}}{dt^2}=\frac{d^3\mathbf{s}}{dt^3}</math>

These common names correspond to terminology 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 series]], enabling several analytical techniques in engineering and physics. The fourth order derivative is called [[jounce]].