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Assumptions:

 1. x(0) <code> 0; x(T) </code> X

 2. v(0) <code> 0; v(T) </code> V

 3. d(a)/dt <= 0

Solution:

 a(t) <code> constant </code> A <code> V^2/2X which implies T </code> 2X/V.

Proof:

Consider assumptions as they apply to f(t) = A * t - v(t):

 1. integral from 0 to T of f = 0

 2. f(0) <code> f(T) </code> 0

 3. d^2(f)/dt^2 <= 0

From the mean value theorem, f(t) = 0.  QED.
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