Jerks are even in physics

Hi,
the title is a pun. There are probably jerks yes, but what I want to talk about is physical unit[1] called jerk, it is named like this because jerk not only means, idiot or stupid, but also to move suddenly, because of surprise.


It will be nice, if we first recall that derivation describes the rate of change of something. For example, speed is the first derivative of position because speed describes the rate of change of position, the higher the speed the more position changes!

{\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {x}}}{\Delta t}}={\frac {d{\boldsymbol {x}}}{d{\mathit {t}}}}.

1st derivation of position “compared” to time

In the picture above you can see how speed is defined compared to position (x) and time (t). It is its derivative as I said before. Now of course you can define something, that describes how velocity changes over time. That is called acceleration.

\mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}

Again, “d” simply means derivation and when it is “squared” it means that you need to derive it twice. Acceleration describes, how velocity changes over time.

This is all you might need for daily life. Of course though, scientists defined next derivations, the change of acceleration in time is called jerk. The change of jerk is called jounce the change of jounce is crackle, next follows pop and then possibly lock, drop, shot and put. The SI units of all of these time, position related things are similar. With each derivation you add one to exponent of time.

v=m/s¹
a=m/s²
j=m/s³

and so on..

Just to remind you, if you have lets say “pop”, which is 6th derivation, of 10 m/s^6 you will have a tremendous speed extremely fast. From this next equation it should be pretty clear:

{\displaystyle {\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}}

The power of the higher derivations is that the exponent does extreme changes in a moment. r is the position, v speed, a acceleration… p is pop and t is time.

This is probably not used much, if at all, even in engineering.. but hey, fun!

Dragallur

[1]It is not a unit. It is physical quantity or something like that. I do not really know how it is called in english.

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