Why does the distance traveled by a falling object increase with the square of time?

Galileo Galilei discovered that falling objects undergo constant acceleration, meaning their speed increases at a steady rate over time.12

Because the speed of a falling object increases in direct proportion to the time spent falling, the total distance traveled is the result of this accumulating velocity. Mathematically, when an object starts from rest and experiences uniform acceleration, the distance it covers is proportional to the square of the elapsed time.2

Galileo confirmed this principle by observing balls rolling down inclined planes, where he noted that the motion remained uniformly accelerated regardless of the incline's angle. He deduced that this same constant acceleration applies to objects in free fall, independent of their mass. This discovery was a significant departure from Aristotelian physics, which incorrectly suggested that the speed of a falling object was proportional to its weight.23