Limitations of Derivative Polynomials

Why not use more terms?

greater bandwidth required

greater computational complexity

less accurate prediction since higher order terms are harder to estimate and errors have disparate impact

In many cases, More terms make things worse.

Example of second order polynomial equation : over time, the equation is more sensitive to the acceleration term than to the velocity term

Moreover, it is harder to get accurate instantaneous  information about higher order derivatives (a user typicallt only controls an object's velocity and acceleration

The Jerk is all about human behavior

Do not take into account capabilities or limitations of objects.