In physics, jerk, jolt (especially in British English), surge or lurch, is the rate of change of acceleration; that is, the derivative of acceleration with respect to time, the second derivative of velocity, or the third derivative of displacement. Jerk is defined by the following equation:

\vec j=\frac {\mathrm{d} \vec a} {\mathrm{d}t}=\frac {\mathrm{d}^2 \vec v} {\mathrm{d}t^2}=\frac {\mathrm{d}^3 \vec r} {\mathrm{d}t^3}

where

\vec a is acceleration,

\vec v is velocity,

\vec r is displacement

\mathit{t} is time.

Jerk is a vector, and there is no generally used term to describe its scalar magnitude.

The units of jerk are metres per second cubed (Metres per second per second per second, m/s³ or ms^-3). There is no universal agreement on the symbol for jerk, but j is commonly used.

Related concepts

Yank is sometimes used as the analog of force with respect to jerk: mass times jerk, or equivalently, the derivative of force with respect to time.^[1]

Higher derivatives of displacement are rarely necessary, and hence lack agreed-on names. The fourth derivative of position was considered in development of the Hubble Space Telescope's pointing control system, and called jounce. Many other suggestions have been made, such as jilt, jouse, jolt, and delta jerk. As more distinct terms that start with letters other than "j", the term snap has been proposed for the 4th derivative of position, with "crackle" and "pop" having been suggested ? facetiously ? as names for the 5th and 6th derivatives.^{http://sprott.physics.wisc.edu/pubs/paper229.pdf}

Footnotes

1. ↑ this is only true non-relativistically; since mass is velocity dependent in relativistic physics, force is usually written as the first derivative of the momentum, while yank would be the second derivative. For force, it can be shown that dp/dt reduces to the familiar ma when v << c.)

References

• Am. J. Phys., Vol. 65, No. 6, Pg. 538, June 1997

External links

• What is the term used for the third derivative of position?, description of jerk in the Usenet Physics FAQ.

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