An Integrating Approach (IA) in the teaching and learning of a first formal course of Mechanics for future engineers and physicists is presented. In this approach, the course is introduced as a practical and technological problem to resolve that delineates a single route during its development. The need to solve the different aspects of the problem leads progressively to establish the contents and concepts of the subject; i.e., these arise as tools to understand and resolve the aforementioned problem. The approach allows to elucidate and assess the approximations, limitations and corrections that must be performed to an own model of a scientific discipline such as physics. The approach potentiality relies in allowing the student, through a concrete and simple problem, to articulate Kinematics, Newton's laws, and Energy, appreciating the subject in a holistic and non-fragmentary fashion. Moreover, it allows the students value Physics and to estimate its usefulness, because they find it useful and necessary for understand the basics behind all technological development, even although it seems very simple. To this purpose, is proposed use a simple device that shoots different masses, through a spring placed on a horizontal surface at a certain height, and measure the distance to which they fall to the floor. This device facilitates the explanation of the physical concepts that emerge in a first analysis of the problem. This approach, as well, facilitates to present in an elegant way the influence of the mass on motion as well as the distinction between constant and variable forces. The experimental results show mass effects according with theoretical predictions, allowing going beyond the usual kinematics taught at this level.