Position of a Particle

To describe motion, we must first define the position of a particle.

In one dimension (along the $x$-axis):

$$ x = x(t) $$

In three dimensions:

$$ \vec{r}(t) = x(t)\hat{i} + y(t)\hat{j} + z(t)\hat{k} $$

The position vector completely specifies the location of a particle at any time.