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The time derivative of acceleration (m/s²) is jerk (m/s³).

I know that when you push on an object, there cannot be true instantaneous acceleration, which leads to infinite jerk, because the object must compress ever so slightly before it starts to move.

However, what if an object is suspended in a vacuum using an electromagnet? When the power is cut, would it release all attractive force instantaneously in exactly no time? Would the jerk be infinite at the moment of the start of free fall? Note: Acceleration will be in standard gravity.

Also, what if the object is hung by a string, and the string snaps due to too much tension (for example, object too heavy)? Will the jerk be infinite?

Also, how about snap (m/s⁴) and crackle (m/s5)?

Qmechanic
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  • If any derivative of the function describing the evolution of a system is discontinuous then you lose the ability to approximate that state with a Taylor series. That might be OK, but you would have to work fairly hard to show that it is. Physically, if things are claimed to happen discontinuously then my intuition just sounds huge alarms: perhaps it is wrong, but I don't think so. –  Aug 10 '17 at 08:15
  • Possible duplicates: https://physics.stackexchange.com/q/151399/2451 , http://physics.stackexchange.com/q/35674/2451 , http://physics.stackexchange.com/q/9720/2451 , http://physics.stackexchange.com/q/1324/2451 and links therein. – Qmechanic Aug 10 '17 at 08:30
  • All measurements have finite precision, which means that we are unable to distinguish "instantaneous" from "very short" processes in principle. Mathematical models of physical processes are idealizations, which means that not all mathematically meaningful questions about them are physically meaningful. Whether something is smooth, instantaneous, irrational, Lebesgue measurable, etc., are among the physically non-meaningful. There are models that involve "instantaneous" jumps, but they are observationally equivalent to models with very steep but smooth changes. – Conifold Aug 10 '17 at 09:03
  • A magnetic field cannot be abruptly put into existence, nor abruptly quenched, because the field contains energy, and finite-power sources and sinks have to change the energy at a limited rate. There is always some electrical resistance, and inductance, and an L/R time constant when you put the crowbar across the power supply. – Whit3rd Aug 10 '17 at 10:00
  • Related : Instantaneous cause – sammy gerbil Aug 10 '17 at 10:07

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