Question

Is the rate of change of acceleration with time important to mechanics?comment.

Answer 1

Yes, absolutely. Not just the rate of change of acceleration but the rate of change of rate of change of acceleration matters as well. And so on in fact, all subsequent rates of changes, until you get a quantity which doesn't change, which you may not necessarily get.

Thankfully however all of this information is encoded in the acceleration itself so we don't have to keep track of all these nth derivatives. If acceleration is given as a function of time t, then we implicitly know all its derivatives.

Checkout what Taylor series of a function is. It gives the relation between the value of a function and it's nth order derivatives.

If you are wondering why don't we see the rate of change of acceleration often in physics then the reason is that Newton's laws help give us the acceleration directly from forces and we have been able to work out the force laws for most forces.

Answer 2

Yes, absolutely. Not just the rate of change of acceleration but the rate of change of rate of change of acceleration matters as well. And so on in fact, all subsequent rates of changes, until you get a quantity which doesn't change, which you may not necessarily get.

Thankfully however all of this information is encoded in the acceleration itself so we don't have to keep track of all these nth derivatives. If acceleration is given as a function of time t, then we implicitly know all its derivatives.

Checkout what Taylor series of a function is. It gives the relation between the value of a function and it's nth order derivatives.

If you are wondering why don't we see the rate of change of acceleration often in physics then the reason is that Newton's laws help give us the acceleration directly from forces and we have been able to work out the force laws for most forces.

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