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Introduction of displacement / distance



To all,

Again this year I began mechanics describing the distinction between
distance and displacement. The example is often a 3-4 othogonal path. My
purpose here is mostly to give easy examples to vectors. Then I quickly and
happily follow with statics and the equilibrium of forces...

While following the teaching I recall, I'm afraid to miss the point on
distance vs displacement. I fell that I force feed my students on that
notion. Do you have suggestions to restore the coherence of my teaching on
that matter. I fail to grasp either:
a) a fluid approach throught distance, displacement and statics, or
b) the fundamental purpose around the distance / displacement distinction.

Here are 3 ideas I'm juggling with:

1- Introducing distance vs displacement with a tentative description of a
projectile launch at an angle. While some naive illustration of the
projectile's trajectory can be made, we can only take a few quantitative
datas such as range. The range would be an example of horizontal
displacement as opppose to the path's distance. But here, displacement
addition makes no sense.


2- Introducing distance vs displacement with a shortest path type of
problem: a 4 points "Travelling salesman". This will have the advantage to
intuitively introduce vector addition. Here, the notion of distance is a
not generalized.

3- Introducing distance vs displacement in the discussion of reference
frame. While positions might differ, displacement in 2 different still
frames are constant. In galilean frames, the distance perceived by an still
observer = V object * t + V frame * t.

Mathieu