Can acceleration be relevant of third derivative?

[player1_1_1]

Homework Statement

can acceleration be relevant of third derivative? something like $$m\ddot{x}=k\dddot{x}$$

 

[collinsmark]

The third time-derivative of position, which is also the first time-derivative of acceleration, is often called "jerk." Anytime you have a system that does not have constant acceleration, you have jerk. Anytime the acceleration changes, you have jerk. So the simple answer to your question, is yes.

But there are no limits to jerk in Newtonian mechanics. Infinite velocity doesn't make much sense, and you can't have infinite acceleration of a massive object because that would imply infinite force. But there are no such restrictions for jerk. Jerk can be modeled as infinite, such as when a non-zero constant force/acceleration is initially applied to an object. (Now whether jerk is actually ever truly infinite in nature, I'll leave that for you to think about. But it certainly can be modeled that way in Newtonian mechanics -- that's my point.)