" It is obvious that, as the piston moves from TDC to BDC and back, the velocity is constantly changing, and that the piston velocity is zero at TDC and BDC. "
" Note again that at TDC and again at BDC, the piston velocity is zero, because the piston reverses direction at those points, and in order to change direction, the piston must be stopped at some point. "
A flat earther has to prove to himself that the earth is round, no matter how much technical information is presented to show that it's true.
It was never a question as to what the Velocity is at some set point in the time domain. At any POINT (t) you can get position, velocity, and acceleration. Position nor Velocity tells whether or not the object is in motion. For this we look at differentials.
In differentials if there is no
change in position for
any time period, then the object
has no motion. Notice I did not say some point in time.
Here example of object in motion but changes direction (does a 180).
t0=0 x=-0.5 v=100
t1=1 x=0 v=0
t2=2 x=-0.5 v=-100
In the tome domain
t0 to t1, dx=0.5, dv=100
t1 to t2, dx=0.5, dv=100
now cross over v=0
t0 to t2, dx=1, dv=0
how about being real real close to x=0
t1a=t1-[some small #] to t1b=t1+[some small number]
at t1a x1a=0-[some small number]
at t1b x1b=0+[some small number]
dx still does not equal zero, thus dx/dt is not zero, aka not at rest for that dt
No matter what small # to subtract from or add to t1, dx will always be non-zero, hence still in motion.
This proves that there is no dt where dx=0, even when dt spans time t where v=0.
Points in time do not define motion, only changes in time do.
So when would it be stopped?
Like this.
For all times between t0 and t1
t0=0, x=0, v=0
t1=1, x=0, v=0
Thus no change in position, no movement, stopped.
