# Motion along a straight line

The trajectory of a point that moves in a linear motion is a straight line. An origin and a direction are set arbitrarily on the line, so that the motion of this point can be described by the coordinate ${\displaystyle x=x(t)}$ (motion in one dimension).

The variation of position of the point with time defines the velocity; the variation of the velocity with time is defined as acceleration.

### Velocity

Definition: Average velocity is defined as the ratio between the displacement and the interval of time (in which the displacement occurs):

${\displaystyle V_{m}(t_{1},t_{2})={\frac {\Delta x_{12}}{\Delta t_{12}}}={\frac {x_{2}-x_{1}}{t_{2}-t_{1}}}={\frac {x(t_{2})-x(t_{1})}{t_{2}-t_{1}}}\ .}$