Velocity, Acceleration, Jerk, Snap, Crackle, and Pop! — Derivatives of Distance

According to Wikipedia, the derivatives are as follows. The quantity \mathbf{x} is bold face to indicate it is a vector: it has both a magnitude and direction.

\begin{array}{cl} \mathbf{x} & {\rm Distance/Position} \\ \frac{d\mathbf{x}}{dt} & {\rm Velocity} \\ \frac{d^2 \mathbf{x}}{dt^2} & {\rm Acceleration} \\ \frac{d^3 \mathbf{x}}{dt^3} & {\rm Jerk} \\ \frac{d^4 \mathbf{x}}{dt^4} & {\rm Snap} \\ \frac{d^5 \mathbf{x}}{dt^5} & {\rm Crackle} \\ \frac{d^6 \mathbf{x}}{dt^6} & {\rm Pop} \\ \end{array}

and adds that the names for the last three derivatives are used “sometimes somewhat facetiously”. Fortunately, there is a jingle to help remember them.

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