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26 January 2014 @ 12:17 pm
Thing that I learned yesterday (one among many, but this is the most memorable):  
The first derivative of distance related to time (change in distance over time) (dx/dt) is velocity.

The second derivative (change in velocity over time) (d2x/dt2) is acceleration.

The third derivative (change in acceleration over time) (d3x/dt3) is jerk.

I knew all of those.

The fourth derivative is jounce.

The fifth, sixth, and seventh derivatives are snap, crackle, and pop.

This makes me very happy.
The Renaissance Manunixronin on January 27th, 2014 12:36 am (UTC)
I don't think you can just go from jerk and time directly to distance. You'd have to integrate under the curve.
Shadow/Brookekengr on January 27th, 2014 02:29 am (UTC)
If it's *constant* jerk, then you can. Just like you can get distance from constant acceleration. My calculus isn't up to it, but someone whose calculus was up to it worked out the formula for me.

You *do* realize that derivatives and integrals can be calculated for various curves?

anyway, look at these formulas.

For constant velocity:

For constant acceleration

for constant jerk
d=(j*t^3)/6 (I looked up the formula in my notes)

The Renaissance Manunixronin on January 27th, 2014 05:39 am (UTC)
Don't you think constant jerk is a bit of a special case though? When are you ever going to encounter it in the real world at any value other than zero?
Shadow/Brookekengr on January 27th, 2014 11:36 am (UTC)
Constant *anything* is a special case.

But jerk is apparently constant enough in some situations for engineering types to have named it.