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Physics LibreTexts

8.4: Higher Derivatives

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Occasionally one may have a use for higher derivatives of position with respect to time. The time derivative of acceleration is called jerk, and the time derivative of jerk is called jounce. One published paper 1 whimsically named the fourth, fifth, and sixth derivatives of x "snap", "crackle", and "pop" after the cartoon characters on boxes of Rice Krispies ® breakfast cereal.

We will seldom, if ever, have need of these higher-order derivatives of x for this course, but for reference, they are summarized in Table 8.4.1.

Table 8.4.1. Time derivatives of position.

Derivative Symbol Name
0 x position
1 dx/dt velocity
2 d2x/dt2 acceleration
3 d3x/dt3 jerk
4 d4x/dt4 jounce, snap
5 d5x/dt5 crackle
6 d6x/dt6 pop

1. Visser, Matt. Jerk, Snap, and the Cosmological Equation of State. Classical and Quantum Gravity, 21 (11): 2603-2616.


8.4: Higher Derivatives is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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