Keith wrote:
"---you need to explain why you do not reject instantaneous velocity,
acceleration, ---."

I don`t reject instantaneous anything including power. Instantaneous
power is not particularly useful in working with radio transmission
lines.

Like infinity, the infinitesimal is unmeasurable. Like infinity, the
infinitesimal is useless in calculations. The idea of the infinitesimal
is useful in perceiving targeted values approached as a variable
approaches a limit.

A differential "d" is an infinitesimal smaller than a difference. "dy"
is the differential of y. "dx" is the differential of x. "dt" is the
differential of t. The ratio "dy/dx" is a slope defined at a point and
is equal to the limit as x goes to zero of the ratio delta y over delta
x.

The basis of differentation is superfluous to this discussion, but Keith
asks, why not reject things which are a derivative with respect to time
including acceleration.

Acceleration may be a good example. Calculus can give the rate at which
a variable varies. On the other hand, it can give a function if the rate
of change is given.

Velocity is the variable in acceleration. Assume velocity is increasing
and you have a definition of the function. For a given velocity the
acceleration can be determined, and for a given acceleration, the
velocity can be determined.

My point, repeated again, is that when delta time is zero, no distance
is traversed, not that acceleration and velocity are zero.

Power x time = energy. Thast`s how the electric power company calculates
your bill. If no time elapses during which power is available, no energy
is consumed.

Best regards, Richard Harrison, KB5WZI