As speed increases for an object in free fall, does acceleration increase also?

Solution 38E The acceleration is defined as the rate of change of velocity. That is if the rate of change remains constant, that is if the equal amount of velocity increases in equal amount of time, then the acceleration remains constant. So, even if the speed of an object increases, the acceleration can be constant. In case of the freely falling body the acceleration remains constant through out of its motion (provided the height from which the object is falling is not comparable to the radius of the earth). No, in the free fall the acceleration does not increase.