Seems like a part 2 with more complex animations would be needed.
[1] http://research.microsoft.com/apps/pubs/default.aspx?id=1917...
Ever tried to play really old games like Worms 1 on anything faster than 100MHz? They are "framerate locked" which means that a higher framerate makes everything go faster. So if you used that function on a 120hz display everything would run at twice the speed (assuming it's designed to run on 60hz). This is why things like Dos Box let you run at a lower emulated CPU frequency: so that you can slow things down so that these games are playable.
In terms of UI animation the most sensible thing to use is Euler Integration (pronounced "oiler").
Euler Integration is based off of Distance = Speed / Time. Basically what you need to do is remember the "last time" the function was called (using a high resolution timer) and find the difference between that and the current frame. This gives you the "Time" in Euler Integration, your "Speed" should be a fixed constant (e.g. 1 pixel per second). Then simply add Distance / Speed to your current X value.
Things git a tad bit complicated to ensure that you don't "overshoot" your target position, but it's nothing simple high-school algebra can't solve (that's the nice thing about Euler Integration, it's all high school Mathematics and Physics).
Techniques like ease-in/ease-out are easy to do (using the difference in distance between the current point and starting/ending points use base your speed off of that), all using high school algrebra.
I wouldn't bother with Verlet or Runge-Kutta: it is just UI animation after all - you aren't going for very accurate results like games do. "Real" physics engines also have the problem of not being able to guarantee deterministic results.
While he is correct about the fact that standard tooling doesn't deal with "distances", he must at the same time give the right solution.
By the way, another more direct way to get it right would be to solve S=D/T for T and hand that to the UI framework. I'm not sure what language/framework he is using but here is the general idea:
speed = 10; start = 0; end = 100; time = (end - start) / speed;
circle.left = start; animate duration: time { circle.left = 100 }
Which in itself has very little to do with a physics engine, but won't result in a customer logging a bug about how things are behaving strangely on their 120hz monitor.
http://themeforest.s3.amazonaws.com/74_jquery/jquerygravitys...
I don't think the author is saying everyone should use a physics engine now. I think he means that we should use real-world physics as a guide to making more realistic animations, be it with a simple effects library or a full-fledged physics engine.
The examples were also a lot more compelling than in this one. If someone can find it it would be great!
Note that box2djs is also very capable[2], and has been around for years (it is port of Erin Catto's great work on Box2D[3]).
[1] http://subprotocol.com/2013/04/18/introducing-verlet-js.html
could this become the next incarnation of skeuomorphism?