Any vector
in two dimensions can be represented as
and
are unit vectors in the x and y directions respectively.
In general, motion is not one dimensional. It is either two or three dimensional. If the motion is in two dimesions,
we can represent the position of a particle at any time by the vector
and we can represent the velocity at any time by the vector
and we can represent the acceleration at any time by the vector
The extension to three dimensional motion is obvious.
Conversely, we can integrate an expression for acceleration to obtain an expression for velocity, and integrate an expression for velocity to obtain an expression for displacement.
The SUVAT equations of motion can also be written in vector form, if the acceleration of the motion is constant.
