# Pop (physics)

In physics, **pop**, also known as **pounce**, is the sixth derivative of the position vector with respect to time, with the first, second, third, fourth, and fifth derivatives being velocity, acceleration, jerk, snap, and crackle, respectively; pop is thus the rate of change of the crackle with respect to time.^{[2]}^{[3]} Pop is defined by any of the following equivalent expressions:

The following equations are used for constant pop:

where

- : constant pop,
- : initial crackle,
- : final crackle,
- : initial snap,
- : final snap,
- : initial jerk,
- : final jerk,
- : initial acceleration,
- : final acceleration,
- : initial velocity,
- : final velocity,
- : initial position,
- : final position,
- : time between initial and final states.

The terms *snap* (also referred to as *jounce*), *crackle*, and *pop*—for the fourth, fifth, and sixth derivatives of position—were inspired by the advertising mascots Snap, Crackle, and Pop.^{[3]}

## Unit and dimension

The dimensions of pop are LT^{−6}. In SI units, this is m/s^{6}, and in CGS units, 100 Gal per quartic second. This pattern^{[clarification needed]} continues for higher order derivatives.

## References

**^**Janzen, Ryan; Mann, Steve; et al. (2014). "Actergy as a Reflex Performance Metric: Integral-Kinematics Applications".*Proceedings of the IEEE GEM 2014*: 311–2. doi:10.1109/GEM.2014.7048123.**^**Thompson, Peter M. (5 May 2011). "Snap, Crackle, and Pop" (PDF).*AIAA Info*. Hawthorne, California: Systems Technology. p. 1. Retrieved 3 March 2017.The common names for the first three derivatives are velocity, acceleration, and jerk. The not so common names for the next three derivatives are snap, crackle, and pop.

- ^
^{a}^{b}Visser, Matt (31 March 2004). "Jerk, snap and the cosmological equation of state" (PDF).*Classical and Quantum Gravity*.**21**(11): 2603–2616. arXiv:gr-qc/0309109. Bibcode:2004CQGra..21.2603V. doi:10.1088/0264-9381/21/11/006. ISSN 0264-9381. Retrieved 17 May 2015.Snap [the fourth time derivative] is also sometimes called jounce. The fifth and sixth time derivatives are sometimes somewhat facetiously referred to as crackle and pop.