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In physics, yank is the derivative of force with respect to time.[1] Expressed as an equation, yank Y is:

$\mathbf{Y}=\frac{\mathrm{d}\mathbf{F}}{\mathrm{d}t}$

where F is force and $\frac{\mathrm{d}}{\mathrm{d}t}$ is the derivative with respect to time $t$.

The term yank is not universally recognized but is commonly used.[citation needed] The units of yank are force per time, or equivalently, mass times length per time cubed; in the SI unit system this is kilogram metres per second cubed (kg·m/s3), or Newtons per second (N/s).

## Relation to other physical quantities

Newton's second law of motion says that:

$\mathbf{F}=\frac{\mathrm{d}\mathbf{p}}{\mathrm{d}t}$

where p is momentum, so if we combine the above two equations:

$\mathbf{Y}=\frac{\mathrm{d}\mathbf{F}}{\mathrm{d}t}=\frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{\mathrm{d}\mathbf{p}}{\mathrm{d}t}\right)=\frac{\mathrm{d}^2\mathbf{p}}{\mathrm{d}t^2}=\frac{\mathrm{d}^2(m\mathbf{v})}{\mathrm{d}t^2}=\frac{\mathrm{d}^2 m}{\mathrm{d}t^2}\mathbf{v}+2\frac{\mathrm{d}m}{\mathrm{d}t}\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t}+m\frac{\mathrm{d}^2\mathbf{v}}{\mathrm{d}t^2}$

where $m$ is mass and v is velocity. If the mass isn't changing over time (i.e. it's constant), then:

$\mathbf{Y}=m\frac{\mathrm{d}^2\mathbf{v}}{\mathrm{d}t^2}$

which can also be written as:

$\mathbf{Y}=m\mathbf{j}$

where j is jerk.

## References

1. Gragert, Stephanie (November 1998). What is the term used for the third derivative of position?. Usenet Physics and Relativity FAQ. Math Dept., University of California, Riverside. Retrieved on 2008-03-12.