Galileo's most famous experiment related to velocity wasn't actually measuring the speed itself, but rather focused on understanding how falling objects accelerate due to gravity.

• The Challenge: It was difficult to accurately measure the high speeds of freely falling objects in Galileo's time.

• The Slanting Solution: Instead, Galileo studied objects rolling down inclined planes. He believed the motion on a ramp mirrored that of a falling object but at a slower pace.

• The Experiment: Galileo would roll balls down polished inclines of varying lengths and measure the time it took for the balls to travel specific distances.

• The Discovery: Through repeated trials, Galileo observed that the time it took for the ball to roll a certain distance was proportional to the square root of that distance. This meant the velocity increased steadily as the ball rolled down the incline due to gravity.

This experiment wasn't directly about measuring velocity, but it laid the foundation for understanding how gravity affects the speed of falling objects. It also helped pave the way for Isaac Newton's laws of motion, particularly the concept of constant acceleration.