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In attempt to prove Newton's linear equation using several methods. New formulae were obtained for eight rectilinear motion and several other new formulae were obtained for linear momentum, energy, power, and projectiles.Newton's linear equation of motion is related to other physical quantities in mechanics. They include: work, energy, impulse, linear momentum, power and projectiles.Little modification of linear equation, will affect these quantities, leading to new formula that will better explain them.