Abstract
This paper presents a simple geometric derivation of the equations of motion for an object that accelerates from zero speed towards 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 Theory of Special Relativity, with the exception of the expression for time dilation, in case the clock postulate is not applied. The clock postulate is used by Special Relativity and 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 longitudinal acceleration, and an alternative expression for accelerated time dilation is presented without the need for the clock postulate
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