[Karellen]

> > they are both shedding energy at the same rate per unit distance.

> Interesting (and I think very reasonable) first-order assumption.

Really? That triggered alarm bells in my head immediately. I mean, it might be true, but I'd need to do the math to figure it out one way or another.

> the calculation could assume the braking force is proportional to velocity, which I think is roughly true of friction generally

Again, not my intuition at all. I'd have gone with the braking force being constant at non-zero velocity. (And force is variable up to the limit of static friction when at zero velocity.)

[calfuris]

Your intuition about braking force matches the thing that triggered alarm bells in your head: work = force x distance, so if the force is approximately constant the kinetic energy dissipated will be approximately constant per unit distance.