Why do moving back and forth, and moving in a circle look the same on a graph of position versus time?

  one dimension of motion on a circle is "back and forth"

Explanation:

Whether the position graphs look the same or not is a function of the acceleration (and velocity), and how position is measured.

For a circle centered at the origin, uniform motion around the circle will be equivalent to sinusoidal motion in the x- or y-directions. So, that motion is equivalent to sinusoidal motion "back and forth", however it may be generated.

The "back and forth" motions of a piston in a cylinder (connected to a crankshaft), and of a pendulum, are almost sinusoidal, but not quite. Their position graphs will differ slightly from the graph of position of an object moving around a circle.

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On the other hand, if the circular motion is plotted as the length of the radius versus time, it will be a constant -- not "back and forth" at all.

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In short, plots of similar motion will look similar.

car a and b are moving in opposite directions

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