According to Galileo, what relationship between distance traveled and time exists for freely falling objects?

The correct choice highlights that, according to Galileo's observations, the distance traveled by a freely falling object increases quadratically with time rather than linearly. As an object falls under the influence of gravity, it accelerates due to the constant gravitational force acting on it, which means that the distance covered during each successive time interval increases.

Galileo established that the distance ( s ) an object falls from rest is proportional to the square of the time ( t ) it has been falling, which can be expressed mathematically as ( s \propto t^2 ). In practical terms, this means that if an object falls for a longer period, it will cover significantly more distance over time than simply increasing in a straight line.

This concept is fundamental to understanding motion under constant acceleration and is a cornerstone in the study of kinematics, distinguishing it from relationships where distance might be inversely proportional, independent, or decrease over time. Such alternatives do not accurately represent the behavior of a freely falling object, as established through Galileo's pioneering experiments and insights into the motion of objects under gravity.