# Abseleration, absity, absition… Jerk, snap, crackle, pop

A couple of the derivatives and integrals of position $\vec s$ are the following. We do not assign them symbols here as they are rare:

• Abseleration is the integral of absity: $\int\int\int \vec s\,\mathrm dt \,\mathrm dt \,\mathrm dt$ with units of $\mathrm{m\cdot s^3}$,
• absity the integral of absition: $\int\int \vec s\,\mathrm dt \,\mathrm dt$ with units of $\mathrm{m\cdot s^2}$, and
• absition the integral of position: $\int \vec s\,\mathrm dt$ with units of $\mathrm{m\cdot s}$.
• Jerk is the derivative of acceleration: $\frac{\mathrm d^3\vec s}{\mathrm dt^3}$ with units of $\mathrm{m/s^3}$,
• Snap the derivative of jerk: $\frac{\mathrm d^4\vec s}{\mathrm dt^4}$ with units of $\mathrm{m/s^4}$,
• Crackle the derivative of snap: $\frac{\mathrm d^5\vec s}{\mathrm dt^5}$ with units of $\mathrm{m/s^5}$, and
• Pop the derivative of crackle: $\frac{\mathrm d^6\vec s}{\mathrm dt^6}$ with units of $\mathrm{m/s^6}$.