There are some limitations in Newton’s law. Which explain in below.
I. When the acceleration are very small (below a few times 10‾¹º ms‾²) Newton’s law does not hold well. In particular, it has been proposed that for these very small accelerations, the force is proportional to a² instead of a.
II. According to special theory of relativity Newton’s law does not hold good. Special relativity teaches us that we cannot extrapolate the use of Newton’s laws to particles moving at speeds comparable to the speed of light.
III. General theory of relativity shows that we cannot use Newton’s law in the vicinity of extremely massive objects.
IV. According to Quantum mechanics Newton’s law is not good to explain the physics. Quantum mechanics teaches us that we cannot extrapolate Newton’s laws to objects as small as atoms.
V. Chaotic universe does not explain by Newton’s law.