I’ve been thinking a bit about rate of change and I read that there are higher order derivatives of a position (like jerk, snap, crackle and pop) which had me confused. The concepts of velocity and acceleration are easier to understand because they are common. I realize though that acceleration etc also ought to be able to have a rate of change but I don’t understand the purpose or usage.
It also had me thinking, is there a limit to what order or how “far” a position can be recursively differentiated? It seems to me that the higher order derivatives perhaps would explain the origins of motion in more detail?
In: Physics
For a real-world example, imagine two cars at a red light, ready to go.
When the light goes green, driver A mashes the pedal to the floor. Driver B does it like he was taught in driver ed — pushing the pedal down to the floor smoothly, ‘like you have an egg under your foot’.
B will trail A, but not by much, in reaching peak acceleration, and thus in speed and distance travelled.
But his passengers will have had a much more comfortable ride without that jerk at the beginning.
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