Flag: slow fall for seeing & hearing time between bells. Spacebar: photo of Galileo's ramp for slowing fall. Shows ball's distance travelled is square of time. Ball descends by v (velocity), v increases by v rate of change. Simple. Few code blocks.
Bells placed at distances that are the square of time. The bells ring a steady rhythm, due to acceleration. I slowed acceleration to allow time to see and hear equal time intervals to travel 1, 4, 9, 16, revealing the distance as square of time. Galileo first did this with a ramp to slow the descent of ball, slowing a with that shallow incline. Equal time between distances 1, 4, 9, 16 (distance is square of time 1, 2, 3, 4). Each timestep, ball descends by v and v increases by velocity rate of change. I set bells at 1, 4, 9, 16 distance units, squares of 1, 2, 3, 4 time units. Each time unit, a bell rings (y = t^2) Galileo did essentially this, with his ramp and bells to show distance as function of time squared. I saw his ramp and bells in a museum in Florence. Spacebar shows it. Velocity is a simple function of velocity rate of change (acceleration). We distance cumulate over time. Galileo used his "Inclined Plane" with small bells, along with a pendulum to provide an experimental demonstration of the law of falling bodies, with the pendulum connected to the inclined plane, acting as a "timepiece". The experiment consisted of releasing a ball from the top of the plane at the same time as the pendulum was swung. For each complete period of the pendulum, the ball would strike one of the small bells placed along the inclined plane at increasing distances, specifically arranged in the order of odd number distances. The experiment made it possible to measure the increase in the distances traveled by the ball as it rolled through equal time intervals starting from the rest position. The ringing bells would also provide an additional auditory observation of the ball's constant acceleration during its fall. Spacebar for photo of that.
