I thought about talking about derivatives but wanted to avoid to mention to many unexplained words, but yes, derivatives are exactly the way you should be thinking about this.

In physics/mechanical engineering they have even names for these derivatives when we talk about motion (in this order):

  position
  velocity
  acceleration
  jerk
  snap
  crackle
  pop  
  

Also see: https://en.wikipedia.org/wiki/Jerk_%28physics%29

Exactly.