Accelerated Motion Towards Relativistic Velocities Described by Newtonian Mechanics

This paper presents a simple geometric derivation of the equations of motion for an object that accelerates to a relativistic velocity. This is not done by using the Theory of Special Relativity, but with Newtonian Mechanics only. The results are identical to those derived by the Special Theory of Relativity, with the exception of the expression for time dilation. It is shown that this discrepancy is caused by a violation of the clock postulate, which is required by Special Relativity, and which assumes that the time dilation of an accelerating object at any moment in time depends on its contemporary velocity only. It is shown that the clock postulate is violated in case of continuous acceleration, and an alternative expression for accelerated time dilation is presented without the need for the clock postulate.