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Fourth, fifth, and sixth derivatives of position#Sixth derivative

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+#REDIRECT [[Fourth, fifth, and sixth derivatives of position#Sixth derivative]]
-In [[physics]], '''pop''' is the sixth [[derivative]] of the [[Position (vector)|position vector]] with respect to [[time]], with the first, second, third, fourth, and fifth derivatives being [[velocity]], [[acceleration]], [[jerk (physics)|jerk]], [[jounce|snap]], and [[Crackle (physics)|crackle]], respectively; pop is thus the rate of change of the crackle with respect to time.<ref>{{cite conference | url = https://info.aiaa.org/Regions/Western/Orange_County/Newsletters/Presentations%20Posted%20by%20Enrique%20P.%20Castro/AIAAOC_SnapCracklePop_docx.pdf | title = Snap, Crackle, and Pop | last = Thompson | first = Peter M. | date = March 2011 | book-title = Proc of AIAA Southern California Aerospace Systems and Technology Conference | page = 1 | format = PDF | access-date = 29 February 2020 | quote = 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. |archiveurl=https://web.archive.org/web/20170304041659/https://info.aiaa.org/Regions/Western/Orange_County/Newsletters/Presentations%20Posted%20by%20Enrique%20P.%20Castro/AIAAOC_SnapCracklePop_docx.pdf |archivedate=2017-03-04}}</ref><ref name="Visser2004">{{cite journal |last=Visser |first=Matt |date=31 March 2004 |title=Jerk, snap and the cosmological equation of state |journal=[[Classical and Quantum Gravity]] |volume=21 |issue=11 |page=2603–2616 |issn=0264-9381 |doi=10.1088/0264-9381/21/11/006 |url=https://arxiv.org/pdf/gr-qc/0309109.pdf |accessdate=17 May 2015 |quote=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.|arxiv = gr-qc/0309109 |bibcode = 2004CQGra..21.2603V }}</ref>  Pop is defined by any of the following equivalent expressions:
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-:<math>\vec p =\frac {d \vec c} {dt}=\frac {d^2 \vec s} {dt^2}=\frac {d^3 \vec \jmath} {dt^3}=\frac {d^4 \vec a} {dt^4}=\frac {d^5 \vec v} {dt^5}=\frac {d^6 \vec r} {dt^6}</math>
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+{{R to related topic}}
-The following equations are used for constant pop:
+}}
-:<math>\vec c = \vec c_0 + \vec p \,t </math>
-:<math>\vec s = \vec s_0 + \vec c_0 \,t + \frac{1}{2} \vec p \,t^2 </math>
-:<math>\vec \jmath = \vec \jmath_0 + \vec s_0 \,t + \frac{1}{2} \vec c_0 \,t^2 + \frac{1}{6} \vec p \,t^3 </math>
-:<math>\vec a = \vec a_0 + \vec \jmath_0 \,t + \frac{1}{2} \vec s_0 \,t^2 + \frac{1}{6} \vec c_0 \,t^3 + \frac{1}{24} \vec p \,t^4 </math>
-:<math>\vec v = \vec v_0 + \vec a_0 \,t + \frac{1}{2} \vec \jmath_0 \,t^2 + \frac{1}{6} \vec s_0 \,t^3 + \frac{1}{24} \vec c_0 \,t^4 + \frac{1}{120} \vec p \,t^5 </math>
-:<math>\vec r = \vec r_0 + \vec v_0 \,t + \frac{1}{2} \vec a_0 \,t^2 + \frac{1}{6} \vec \jmath_0 \,t^3 + \frac{1}{24} \vec s_0 \,t^4 + \frac{1}{120} \vec c_0 \,t^5 + \frac{1}{720} \vec p \,t^6 </math>
-where
-:<math>\vec p</math> : constant pop,
-:<math>\vec c_0</math> : initial crackle,
-:<math>\vec c</math> : final crackle,
-:<math>\vec s_0</math> : initial snap,
-:<math>\vec s</math> : final snap,
-:<math>\vec \jmath_0</math> : initial jerk,
-:<math>\vec \jmath</math> : final jerk,
-:<math>\vec a_0</math> : initial acceleration,
-:<math>\vec a</math> : final acceleration,
-:<math>\vec v_0</math> : initial velocity,
-:<math>\vec v</math> : final velocity,
-:<math>\vec r_0</math> : initial position,
-:<math>\vec r</math> : final position,
-:<math>t</math> : time between initial and final states.
-The terms ''snap'' (also referred to as ''[[jounce]]''), ''[[Crackle (physics)|crackle]]'', and ''pop''{{mdashb}}for the fourth, fifth, and sixth derivatives of position{{mdashb}}were inspired by the advertising mascots [[Snap, Crackle, and Pop]].<ref name="Visser2004" />
-==Unit and dimension==
-The dimensions of pop are LT<sup>−6</sup>. In [[SI units]], this is m/s<sup>6</sup>, and in [[CGS]] units, 100 [[Gal (unit)|gal]] per quartic second.
-==References==
-{{Reflist}}
-{{Kinematics}}
-[[Category:Motion (physics)]]
-[[Category:Physical quantities]]