What is it called when object A is accelerating at rate B, but rate B is also accelerating at rate C. What is it called? How does it work? How can I apply it?
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Motion eqution is given by $f=ma$ Entirely . if $a=a(t)$, the force must be $f=f(t)$. The motion will be $ma=f(t)$, and obviously it doesn't involve the change of acceleration, so don't care it. – Feynman Mar 31 '17 at 00:37
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You don't need to do anything in particular.
The derivative of the acceleration (I don't think it's correct to call it velocity of acceleration, or call the second derivative acceleration of acceleration, just brings misunderstanding) is seldom used, but it's called $\textit{jerk}$ [1]. You can obtain it simply by deriving acceleration with respect to time.
But you always have to keep a particular thing in mind: in classical physics, you should be able to describe the motion of an object using only the motion equation, the initial coordinate and the initial velocity. Motion equation should be a second order differential equation. No derivative of the acceleration is admitted, and no derivative of the position superior to the second derivative. You can't have jerks or derivatives there.
Salvatore Baldino
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