3 ms·
Anecdotal evidence: Ever experienced that a bus is braking (near-constant deacceleration), and people seem fine; but then the bus comes to a halt and thus stop
by setopt 2y ago
Anecdotal evidence:
Ever experienced that a bus is braking (near-constant deacceleration), and people seem fine; but then the bus comes to a halt and thus stops deaccelerating, and people suddenly fall on the floor?
I think at least the derivative or acceleration is important for how well people can compensate. Not sure about higher derivatives though.
- amelius 2y agoAcceleration equals force, so yeah, if you abruptly change acceleration then this equals abruptly changing the force on people in the bus. Acceleration should thus be continuous (not necessarily differentiable). I don't know how you would justify constraints on higher derivatives. Perhaps they mess with our own internal control mechanism?
- ccccccc1 2y agois it physically possible to have non-continuous acceleration?
- shagie 2y agoImagine a multistage rocket and the changes in acceleration. Figure 4-3 in https://www.ibiblio.org/apollo/Documents/lvfea-AS506-Apollo11.pdf https://www.ibiblio.org/apollo/Documents/lvfea-AS506-Apollo1... shows this for Apollo 11.
- zardo 2y agoI imagine if you zoom in far enough on those points you have the acceleration continuously changing as pressure slowly builds in the engines over several microseconds.
- shagie 2y agoI was thinking more of the instant you shut off engines and disconnect 130,000 kg of mass of stage one. There is an interesting Δa/Δt while fuel is consumed and mass changes. There are discontinuities to the graph when engines are shut down and stages decoupled.
- sokoloff 2y agoThat’s the essence of a legitimate question: over small enough time periods (as the bolts explode over a non-zero period of time), is it continuous or discontinuous? Over a macro scale, it’s discontinuous, of course.
- tomek_ycomb 2y agoIt's nature, it's continuous at small enough scales. But, checkout Zeno's paradox for more on your philosophical questions
- setopt 2y agoIf we zoom in on a single electron absorbing the momentum of a single photon, it will accelerate “instantly”. The same goes for e.g. an unstable atomic nucleus that ”splits”. At macroscopic scales, I’m not aware of exactly instantaneous acceleration, since you would need some time to “sync” the movement of each atom in the object. But some processes will of course look instantaneous at any given time scale.
- circuit10 2y agoAren’t you describing infinite acceleration, or discontinuous velocity?
- amelius 2y agoVoltages can change abruptly. Therefore, forces can change abruptly, and hence acceleration as well.
- tomek_ycomb 2y agoI think bus is braking with a constant breaking force. But, the bus has a non-constant kinetic energy (going up with the velocity*velocity, down as velocity goes down.) So, you're actually producing a non-linear acceleration. This is jerk, but you can also think of it as just a non-linear acceleration and people are reacting to the fact it's not at all near constant deacceleration, and this is most noticable as velocity hits zero. So, yes, it's jerk, but no, I think it can be intuitively better understood with pure acceleration terms and no jerk needed