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As we all know, if you differentiate distance with reference to time, you get speed, and likewise, differentiating speed you get acceleration. However, if you keep differentiating, to the rate of change of acceleration and so forth (more emphasis on the so forth): is there any point to this? Does it have any useful application in any industrial or practical industry, as opposed to theoretical physics?

Also, what could we possibly learn about a situation by understanding the rate of the rate of the rate of change of the objects distance?

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marked as duplicate by Dilaton, Emilio Pisanty, Qmechanic Aug 12 '13 at 23:06

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Related: physics.stackexchange.com/q/41243/2451 Possible duplicates: physics.stackexchange.com/q/52024/2451 and links therein. –  Qmechanic May 19 '13 at 23:40
Ahh yes I've just seen this now: physics.stackexchange.com/q/45517 –  Mark Ramotowski May 19 '13 at 23:50

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The amplitude of quadrupole radiation is proportional to the source's value of $d^3 x/dt^3$. This applies to both electromagnetic radiation and gravitational radiation (for which quadrupole radiation is the lowest possible multipolarity).

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