Describe linear motion

A linear motion in a given frame of reference, however, need not always be one dimensional. Consider the motion of a person swimming along a straight line on a calm water surface. Note here that position of the person at any given instant in the coordinate system is actually given by a pair of coordinate (x, y) values.

There is a caveat though. We can always rotate the pair of axes such that one of it lies parallel to the path of motion as shown in the figure. One of the coordinates, y y₁ is constant through out the motion. Only the x-coordinate is changing and as such motion can be described in terms of xcoordinate alone. It follows then that all linear motion can essentially be treated as one dimensional motion.