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 v_f . If this variation of the acceleration can be expressed as a=(g/v^2_f)(v^2_f-v^2) , determine the time needed for the velocity to become v=v_f/2 . Initially the particle falls from rest. Express your answer in terms of the variable v_f and the constant gravitational acceleration g.