Question

I was thinking... IF an object is accelerating, must the model for it's position be a cubic or one of greater degree? if it was any smaller than a degree of 3 than the second derivative would prove to = 0x... just need a yes this is true for all cases or no it isn't.

Answer 1

Nope. At least not from a purely mathematical view. Not all derivatives will decrease to zero, what about 1/x (x^-1) ? or ln(x) or sin(x) or e^x etc. etc.