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I've never had a student gush over the algebra that leads to delta X
= Vo t + 1/2 a t^2
But I have seen many happy faces when we explain that the Vo t is a
rectangle and the 1/2 a t^2 is a triangle, and the formula gives the
area of the trapezoid on the V vs t graph. In fact, before we cover
that, I show them the geometric meaning of (x+y)^2 = x^2 +2xy + y^2.
This is always met with happy astonishment and annoyance that they
were not shown this picture in algebra class.
My point is that the algebra and the geometry dance together. Gotta
do both...