On the Groundless Use of Mathematics Concerning the d’Alembert’s Rule

The paper discusses the groundless use of mathematics. This question has been explained mainly based on example of the so called d`Alembert’s rule which unfortunately still functions in science none the less it has been based on a fiction, contrary to the truth cognition as the fundamental purpose of science. That pejorative feature of the mentioned paradigm is marked very clearly in the paper to evaluate it negatively as the only one possible note. Next the adequate characteristics of variable body motion has been presented and the description of Atwood device given in view of explaining the essence of a real equilibrium of the system of material bodies where their real inertia is of importance. In conclusion the characteristics of real inertia force being the measure of this inertia is presented. The erroneous up-to-date view concerning the measure of body inertia, assuming mass as the measure of this magnitude enabling free manipulation of the acceleration value, has been revealed. At the end it is stressed that acceleration is always positive in its nature and is existent in each condition of the material reality.