Let’s say you want to make a math test more difficult. One of the most basic data you can have about something is how far away it is; distance. The change in the distance is velocity/closing rate. The change in velocity/closing rate is acceleration. What would be the next step?
Also, what is the antonym of “closing rate”, i.e.: not how fast something is coming toward you but how fast it’s going away from you?
Jerk.
No, I’m not insulting you. That’s the answer.
With the next several being Snap, Crackle, and Pop (yes, scientists are fully capable of Dad jokes as well)
It’s derivatives all the way down.
I would say “receding rate”, or if you want to get fancy “recessional velocity”.
Well, jerk involves how I’d answer the OP’s question — the next variable is time. Without time you cannot measure velocity or acceleration.
Velocity is the rate of change of position with respect to time.
Acceleration is the rate of change of velocity with respect to time.
And is time fundamental or emergent?
A very crisp answer - but only works with spherical rice in a vacuum.
I think it’s better than that. As an answer, it’s GRRRRREAT!
I read somewhere that when designing the Hubble Space Telescope, they took into account the first 11 levels of this derivative ladder.
Totally Cool. Thank you!
Said another way, the Hubble probably holds the world’s record for machine gentleness. Unless it’s been eclipsed by some subsequent space telescope.
If so, it was only as part of constructing a power-series expansion of some function. I don’t think anything has ever actually made direct use of snap, crackle, or pop (much less anything further) for any direct purpose.
Nitpick: the rate of change of the distance is the velocity, and the rate of change of velocity is acceleration.
Understanding jerk can make you a better driver/pilot: gradual changes to the positions of the controls (steering wheel, brake/accelerator pedals, yoke/stick/throttle) reduces jerk and makes your passengers more comfortable. For extra credit, work on reducing how hard you brake your car as you approach a complete stop; in the perfect case, your car’s deceleration will gradually approach zero (a low jerk value) as its velocity approaches zero, and you won’t have your passengers and cargo lurching back and forth when you stop completely.
In the ideal stop you’re also slowly relieving the nose-dive in the suspension. So the car halts with no suspension rebound. Automatic transmission pull at idle can make this more difficult than one might wish.
I could always stop with no rebound in my manual transmission cars, my friends with automatics never did. I always assumed it was a matter of lack of skill/consideration, until I started driving an automatic regularly, and found that it is actually much more difficult.
I thought it was “…assuming spherical cows” but carry on. I’ve cleaned up my spilled coffee and refilled.
Yes, pretty much anything with a non-negligible elastic property is affected by jerk because it stores energy during decel and releases it all suddenly when the accel suddenly falls to zero. This includes tires, suspension springs, and the meatbags in the passenger compartment.
Anyone my age will recall the sinking feeling in the pit of their stomach when an up elevator started with too much jerk. I haven’t been in such an elevator in ages.
Huh, I can usually stop without rebound in my car, and I’ve never driven a manual. I didn’t realize that was a superpower (though a friend, who’s an excellent driver and helped teach me, did tell me that doing that was one mark of a good driver).