The difference between time and duration ... yeah, I can see people getting thrown by that. I get it intuitively, so it never occurs to me that someone else wouldn't. It's why I shouldn't be a teacher.

Speed vs.acceleration, though ... that IMO isn't simplifying the concept, it's the problem being asked. In explaining the "confusion" you introduced a new variable which "must be zero". You could just as easily introduce direction and say that *it* must be constant. Also true, but defining all the variables that *could* affect the outcome if they *were* included seems like s different sort of problem.

The "force" example ... yeah, that requires understanding what force *means* as more than just a variable in an equation.

[edit]

I figured out how to explain my thinking better.

You have to understand the units and what they represent for a calculation to be meaningful. I "get" that time means elapsed time; the idea that "3:00 p.m." could show up in that equation just doesn't occur to me.

But in the "force" example, "force" is actually a tricky concept. Tell a student that you apply "the same force" and you've already lost them. The intuitive concept is that "I pushed just as hard", so you would think it takes longer to get the heavier ball up to speed, and therefore you've put more "work" into it, so the kinetic energy would be higher. But the formal definition of "force" doesn't work that way. You've already abstracted away questions of how that force could be efficiently and completely transferred to two different masses. You've also obscured the fact that you wouldn't necessarily be pushing all the way from start to finish.

The correct form of that example if you wanted to teach the concept of force is:

You have two wagons on a frictionless surface with a different amount of weight in them. Each is pulled by a rope that goes around a pulley, up over a second pulley, and down to a hanging weight. (ie: The falling weight pulls the wagon.) The falling weight provides the force. The two wagons will cross the finish line at different times, at different speeds, but with the same kinetic energy because both had the same force applied.