6 ms·

Derivatives of relative displacement as defined by a distance metric in a [e.g. metric tensor] space: Length = Point2 - Point1 Length * Time^-1 = Velocity

Derivatives of relative displacement as defined by a distance metric in a [e.g. metric tensor] space: Length = Point2 - Point1 Length * Time^-1 = Velocity or Speed Length * Time^-2 = Acceleration Length * Time^-3 = Jerk Length * Time^-4 = Snap or Jounce Length * Time^-5 = Crackle Length * Time^-6 = Pop Displacement (geometry) > Derivatives: https://en.wikipedia.org/wiki/Displacement_(geometry)#Derivatives https://en.wikipedia.org/wiki/Displacement_(geometry)#Deriva... Fourth, fifth, and sixth derivatives of position: https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...

jameshart 3y ago
Something weird about this is that humans very often ascribe the sensation of d^ns/dt^n, to feeling d^n-1s/dt^n-1. So people will say that something which accelerates quickly is 'fast'. Or they will say, when they feel themselves initially being pressed back into their seat as a plane starts its takeoff roll, that they are experiencing 'acceleration' when what they are experiencing is actually jerk. The thing is, you can't actually feel motion at a constant speed - so the only thing that tells you you are acquiring speed is your body's experience of acceleration - so when you feel yourself accelerating, you associate that with speed. Likewise, your body also can't really tell the difference between constant acceleration and just... being at a different angle, and maybe a bit heavier than normal. So it's when you experience changes in the apparent direction of 'down' and the overall 'weight' you're feeling that you think 'oh, we're accelerating'. My favorite way to get a sense of what acceleration, jerk and snap feel like is to focus on what happens when you're in a car that's braking hard. You're decelerating at a relatively constant rate while the brakes are applied - it feels as if 'down' is pointing slightly forward, meaning you'd be sliding off the seat if it weren't for your seatbelt holding you back. When the car finally stops though, there's a very abrupt change in acceleration - a 'jerk'. 'Down' switches to pointing straight down again, very quickly. You're pulled back into your seat. That's jerk. And specifically the sudden onset of that swing in what direction 'down' is pointing, and then its rapid disappearance is snap. Your body feels like it's being 'jerked' around when the car stops precisely because that motion has high snap - you experience a sudden high amount of jerk, then the jerk ends.
- pixl97 3y ago
  >The thing is, you can't actually feel motion at a constant speed In a vacuum. If you roll the window down, or if the atmosphere starts ablating you into a hot plasma then you may realize you're going very fast.
  - jameshart 3y ago
    Or the air's going very fast past you. Who can tell?
    - brokencode 3y ago
      Unless you’re in a wind tunnel or a hurricane, you can be pretty confident in the reason for the fast air.
    - pixl97 3y ago
      Well, if you're on a 2D plain, it's pretty easy to tell. If the solid plain is stationary to your motion, then the air is fast. If the solid plain is moving, then it's a little tricker to figure out.
  - lambdasquirrel 3y ago
    Oh cmon, who rolls down the windows in an airplane? ;)
  - uoaei 3y ago
    Then you're experiencing acceleration, just in the opposite direction.
    - jameshart 3y ago
      Not if you’re moving at constant speed. The air molecules are experiencing acceleration.
      - uoaei 3y ago

jameshart 3y ago

Something weird about this is that humans very often ascribe the sensation of d^ns/dt^n, to feeling d^n-1s/dt^n-1. So people will say that something which accelerates quickly is 'fast'. Or they will say, when they feel themselves initially being pressed back into their seat as a plane starts its takeoff roll, that they are experiencing 'acceleration' when what they are experiencing is actually jerk. The thing is, you can't actually feel motion at a constant speed - so the only thing that tells you you are acquiring speed is your body's experience of acceleration - so when you feel yourself accelerating, you associate that with speed. Likewise, your body also can't really tell the difference between constant acceleration and just... being at a different angle, and maybe a bit heavier than normal. So it's when you experience changes in the apparent direction of 'down' and the overall 'weight' you're feeling that you think 'oh, we're accelerating'. My favorite way to get a sense of what acceleration, jerk and snap feel like is to focus on what happens when you're in a car that's braking hard. You're decelerating at a relatively constant rate while the brakes are applied - it feels as if 'down' is pointing slightly forward, meaning you'd be sliding off the seat if it weren't for your seatbelt holding you back. When the car finally stops though, there's a very abrupt change in acceleration - a 'jerk'. 'Down' switches to pointing straight down again, very quickly. You're pulled back into your seat. That's jerk. And specifically the sudden onset of that swing in what direction 'down' is pointing, and then its rapid disappearance is snap. Your body feels like it's being 'jerked' around when the car stops precisely because that motion has high snap - you experience a sudden high amount of jerk, then the jerk ends.

pixl97 3y ago
>The thing is, you can't actually feel motion at a constant speed In a vacuum. If you roll the window down, or if the atmosphere starts ablating you into a hot plasma then you may realize you're going very fast.
- jameshart 3y ago
  Or the air's going very fast past you. Who can tell?
  - brokencode 3y ago
    Unless you’re in a wind tunnel or a hurricane, you can be pretty confident in the reason for the fast air.
  - pixl97 3y ago
    Well, if you're on a 2D plain, it's pretty easy to tell. If the solid plain is stationary to your motion, then the air is fast. If the solid plain is moving, then it's a little tricker to figure out.
- lambdasquirrel 3y ago
  Oh cmon, who rolls down the windows in an airplane? ;)
- uoaei 3y ago
  Then you're experiencing acceleration, just in the opposite direction.
  - jameshart 3y ago
    Not if you’re moving at constant speed. The air molecules are experiencing acceleration.
    - uoaei 3y ago