> > 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.)
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.
> 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.)