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.
