Velocity is what you feel when driving on the highway.
Acceleration is what you feel when you step on the gas and the increase in velocity pushes you into your seat.
How can one intuitively understand the higher order derivatives of velocity: jerk, snap, crackle and pop?
In: Physics
You feel Jerk when you accelerate very suddenly (either hitting the gas pedal or brake hard) as opposed to a smoother acceleration that more experienced drivers get used to doing (or when there’s not a sudden surprise). This is what is likely to cause you to suddenly fling backwards or forwards
I don’t think snap, crackle, and pop have easily-understandable analogs.
Position
Velocity
Acceleration
Jerk
Snap (Jounce)
Crackle
Pop
These are all derivatives of the position vector, there at the top, with respect to time. Each one is a derivative of the last. All it means is the rate of change of the previous.
That means velocity is the rate of change of position, aka “speed”.
Acceleration is the rate of change of velocity. No not only are you changing position over time, but the amount of position you’re changing from one time interval to the next is changing.
Jerk is the rate of change of acceleration. So not only is the amount of position your changing over time itself changing, but the amount of change of change is also changing. If that sounds confusing, it’s meant to be funny, because yes indeed the word play starts to get ridiculous.
Imagine controlling the throttle – you don’t just step on the pedal to a certain point and that dictates how fast you accelerate, that pedal has to travel, from the position it’s in to the position you want it to be, and in that sweep you experience jerk. Acceleration will make you feel g-force – if you want to imagine it, it’s that feeling you’re sunk into your seat. But acceleration is constant, so if you’re accelerating at 15 mph/s, you’re going to be pressed to a certain depth into your seat and no further. You will remain sunk in that seat so long as you’re accelerating. BUT, you have to go from resting on top of your seat back to ACTUALLY SINKING IN, and as your depth into your seat back changes, it can only be achieved by accelerating more and more. That’s JERK.
Each additional derivative is a rate of change in the previous. You can express this in terms of depressing the gas pedal and the nature of how that change over time increases or decreases, you could draw that change over time on a graph – it’s how the graph curves rather than just slopes, but derivatives beyond jerk really don’t apply to much beyond an engineering perspective. I know the higher derivatives have some application in aviation, and that’s the industry engineers responsible for giving them their names after the cereal.
> Velocity is what you feel when driving on the highway.
Thus is incorrect. You can’t feel velocity. You can only feel *changes* velocity, i.e. acceleration.
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