>From the feedback I'm getting regarding curved vectors, I think it's a

bad idea, and will henceforth use the terms "curved components" and

"straight vectors"; or perhaps just let it be implied that components

may be curved or straight, and vectors will always be straight.

In any case, the length depicts the magnitude, the curvature, or lack

thereof depicts the path, and the arrowhead at the end depicts the

direction at that end point.

While "Webster's" does not define a vector as being a straight line, it

seems to be that everyone thinks of them and uses them as straight

lines.

Traditionally, force, displacement and acceleration have been depicted

as straight vectors, and the average displacement of a moving body is

the resultant of two or more vectors. Even though the resultant (a

straight vector) does not depict the actual path of the body, it has

long been considered as representing its average displacement.

Since force, displacement and acceleraion actually vary in both

magnitude, and direction, they can best be depicted with curved

components; all drawn to scale:

The initial velocity of an object can be depicted with a straight

vector, oriented in a convenient, arbitrary direction from a point of

beginning, and its actual resultant path - the evolute - can be

depicted as the arc of an ellipse, also from that same point of

beginning.

The displacement, or displacements will emanate - as an involuted curve

- from a point or points along a straight tangent that is aligned with

the initial velocity vector to points on the resultant arc that are

equadistant from the point of beginning.

These three components form a geometric figure with three sides - two

curved and one tangent - and three angles: an apex angle with two right

angles opposite it. The shape of this figure remains the same

regardless of its size and extent.

Don