Question: When a particle falls through the air, its initial acceleration a = g diminishes until it is zero, and thereafter it falls at a constant

When a particle falls through the air, its initial acceleration a = g diminishes until it is zero, and thereafter it falls at a constant or terminal velocity vf. If this variation of the acceleration can be expressed as a = (g/v²_f) (v²_f - v²), determine the time needed for the velocity to become v=v_f/2. Initially the particle falls from rest.

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