You can use two-dimensional vectors to describe motion in a plane.

If a particle starts from the point with position vector \(\bold{r}_0\) and moves with constant velocity \(\bold{v}\), then its displacement from its initial position at time \(t\) is \(\bold{v}t\) and its position vector \(\bold{r}\) is given by \(\bold{r} = \bold{r}_0 + \bold{v}t\).

Vectors can be written in column notation or \(\bold{i}-\bold{j}\) notation.

For an object moving in a plane with constant acceleration:

\(\bold{v} = \bold{u} + \bold{a}t \)

\(\bold{r} = \bold{u}t + \frac{1}{2}\bold{a}t^2 \)

where

\(\bold{r}\) is the displacement at time \(t\)
\(\bold{u}\) is the initial velocity
\(\bold{v}\) is the velocity at time \(t\)
\(\bold{a}\) is the acceleration