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The research work is aimed at proofing equations of linear motion through normal formula derivation, calculus notations with a new innovation using matrices to express the equation of linear motion: as well as other physical quantities in mechanics such as: force, work, impulse, linear, momentum, pressure and power in a connective manner.It also tries to relate Sir Isaac Newton's (1642 - 1728) laws of motion to the experimental works of the great Italian physicist Galileo Galilei (1564 - 1642).