Coordinate System / Sign Convention

A coordinate system is the chosen origin, axis, and positive direction used to assign signed quantities to a motion situation.

A sign convention is the rule that says which direction is positive and which direction is negative.

The sign convention is not discovered from nature; it is chosen by the modeller. Once chosen, it must be used consistently.

For example, if east is positive, then westward displacement and velocity are negative. If upward is positive, the acceleration of free fall near Earth is usually $a=-g$.