Mechanics of particles and systems Definition

Jerk

Builds on Acceleration Higher derivative

Definition

Let $I \subseteq \R$ be an open interval of times, and let $x \colon I \to \R^3$ give the position of a point particle in a fixed frame of reference. Assume $x$ is twice differentiable on $I$ , with acceleration $a = \ddot x$ , and that $a$ is differentiable at $t \in I$ . The jerk of the particle at time $t$ is the vector $j(t) = \dot a(t) = x^{(3)}(t),$ the third derivative of the position.

Remarks

Example: for $x(t) = (t^3, 0, 0)$ , the acceleration is $a(t) = (6t, 0, 0)$ and the jerk is the constant vector $(6, 0, 0)$ . Non-example: the change of acceleration $a(t_2) - a(t_1)$ is not the jerk; it must be divided by $t_2 - t_1$ and the limit taken. For uniform circular motion with angular speed $\omega$ and position $x(t)$ relative to the centre, $j(t) = -\omega^2 \dot x(t)$ , which is nonzero although the speed is constant. The SI unit of jerk is $\mathrm{m/s^3}$ .

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Derivative concept
Euclidean vector concept
Higher derivative concept
Second derivative concept
Velocity concept
Acceleration concept
Jerk definition

Tag	`YFTMB5EHE7`
URI	`m2://YFTMB5EHE7`
Kind	definition
Writing	W0 stub
MSC	70B05
Defines	Jerk
Uses	Acceleration, Higher derivative
Changed	3 November 2026

Jerk

Definition

Remarks

Reading path

Further reading

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