Let me break it down again.
BTW here is an answer to your ball in the air example.
So if you are talking classical mechanics, which you keep bringing up the displacement curve derived from classical mechanics, you are wrong.
A smooth continuous displacement curve does not mean velocity is never zero. Again take the derivative of the piston's displacement curve and note the points at which it's velocity is zero.You admit the graph describes motion that is continuous then you somehow twist that around to say that it does not mean the velocity is never zero.
I have told you how to mathematically (calculus) and graphically prove the piston's velocity at TDC and BDC of a running engine is zero. These methods are used in classical mechanics and in FEA software that helps simulate and analyze ICE design/operations. BTW the displacement sine curve you keep referring to that describes the pistons displacement over time is derived from classical mechanics.The piston does change direction but it does not become motionless. As soon as the EE I was talking to suggested the best way to look at the problem was imagining a motion of the rotation of the crankshaft and rod bearing journal describing a sine wave then it became clear to me that the piston does not stop.
Why? If you can't explain it either you don't understand the concept, the concept is flawed or requires a different discipline to describe.It is a hard concept to accept. I was convinced it does have to stop -- I dare say it "looks" like it has to stop -- but it doesn't/can't stop.
Lol, sounds like your geometry instructor was speaking outside of classical mechanics an into the realm of quantum mechanics which how the hell did he sketch that on the chalkboard? Sounds like he was discussing the uncertainty principle in which we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy. In that case, nothing is ever at rest except at 0 kelvin in which all particle motion stops and disorder disappears. Simply put you then cannot use your sine wave displacement curve example (derived from classical and not quantum mechanics) to describe the location of the piston, if anything the curve would not be a line but a cloud of infinite points.Years prior I had a rather lengthy discussion with my geometry instructor on the subject of a baseball being thrown straight up in a geometrically straight line. Absent any outside forces other than gravity the ball continues up until it begins to come down again. Of course I believed it had to stop. But the instructor convinced me it did not. I did not copy down what was on the chalkboard.
BTW here is an answer to your ball in the air example.
So if you are talking classical mechanics, which you keep bringing up the displacement curve derived from classical mechanics, you are wrong.