  Newton second law of dynamics is a law of motion but also a useful definition
of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration
and parallelism of force and acceleration. In the special theory of relativity,
out of these three only the description of force (F=dp/dt) does not raise
doubts. The greatest problems are posed by mass, which may be invariant rest
mass or relativistic mass or even directional mass like longitudinal mass. This
results from breaking the assumption of parallelism of force and standard
acceleration. It turns out that these issues disappear if the relativistic
acceleration A is defined as a relativistic velocity subtraction formula. This
basic fact is obscured by some subtlety related to the calculation of the
relativistic differential of velocity. It is based on the direction of force
rather than on transformation to a resting system. The reference to a
non-resting system generates a (seemingly) different velocity subtraction
formula. Thus, the relativistic three-dimensional acceleration is neither rest
acceleration, nor four-acceleration, nor standard acceleration. As a
consequence, inertial mass in any direction of the force has the same value as
relativistic mass. In other words, the concepts of transverse mass and
longitudinal mass, which depend on velocity, have been unified. In this work a
full relativistic equation is derived for the motion of a body with variable
mass whose form confirmed the previously introduced definitions. In addition,
these definitions are in line with the general version of the principle of mass
and energy equivalence. The work presents a detailed review and discussion of
different approaches to the subject in relation to original historical and
contemporary texts. On this basis, a proposal is made for consistent definition
of relativistic quantities associated with velocity change.
