[tsm]

It's absolutely useful to tell 4th-graders that x(t) = vt + x₀ (assuming no acceleration) since they're probably not on top of exponents yet.

It's also absolutely useful to tell 8th-graders that x(t) = at² + v₀t + x₀ since now they can handle exponents.

And it's useful to tell 12th-graders how to do the calculus to get x(t) for variable acceleration.

But that's also inaccurate for very large values of v (or a) due to relativistic effects. However, it's a very convenient simplification ("lie") for the vast majority of people in the vast majority of cases. It's probably possible to explain the relativity math to most 4th-graders, but for most of them it's a terrible use of teaching time and the old "rate times time equals distance" that was drilled into my head at a young age is much more practical.

[bilvar]

> It's absolutely useful to tell 4th-graders that x(t) = vt + x₀

Why is this useful? Where and when are they going to use this equation until they learn the correct one?

[cancerhacker]

In 4th grade I was writing very simple animations in basic on an Atari 400 and I absolutely would’ve used and understood this. I think this is a perfect example of perfect being the enemy of good. (And I think I’m mangling that phrase)

[bilvar]

Fair enough.

[michaelt]

Anything moving horizontally, I guess?

(admittedly that's not what tsm's post implied, but still...)