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It is supposed that the acceleration is known as a function of time and by applying a double integration over this function of time the position of the object can be find, assuming initial zero conditions:
The only mathematical prerequisite is a thorough knowledge of first-year college calculus, including sums of infinite series, differentiation, and single and double integration.
A double integration stage allows the output voltage to be proportional to Acceleration, Velocity or Displacement.
Alpha]z] having opposite sign can be arbitrarily large, and can dominate the whole expression, we can not sign the double integration.
From T2 b), the inner double integration is negative, and so the theorem's forward implication is proved.