2.3 Position

Definition

Position describes where an object is located relative to a chosen reference point.

In everyday life, we often describe position using familiar expressions such as:

  • The café is next to the library.
  • The school is across the street.
  • The hotel is 500 m from the beach.
  • The airport is 15 km north of the city centre.

These descriptions help us identify an object’s location.

In physics, however, position must be described more precisely. A statement such as “The object is 5 m away” is incomplete because it does not specify 5 m from where. In many situations, it should also indicate the direction. Therefore, every position must be described relative to a chosen reference point.

The Origin

The chosen reference point is called the origin.

The origin is the point from which all positions are measured. It may be selected wherever it is most convenient for the problem being studied.

For example, the origin may be:

  • the starting line of a race,
  • the entrance of a building,
  • the centre of a laboratory,
  • the intersection of two roads.

Once the origin has been chosen, every object’s position can be described consistently.

Position in One Dimension

For motion along a straight line, position is represented by a single coordinate on an axis.

In Figure 2.3.1, Object A is at x = -4 m and Object B is at x = +5 m.

Figure 2.3.1 – Positions of two objects along the x-axis.

Object A is located 4 m from the origin in the negative x-direction, while Object B is located 5 m from the origin in the positive x-direction.

The sign of the coordinate indicates on which side of the origin the object is located.

Position in Two Dimensions

For motion on a plane, one coordinate is not sufficient.

In two dimensions, position is represented by an ordered pair,

(x,y)(x,y)

where x and y are measured from the origin along the x- and y-axes.

For example, the position (3, 2) means the object is located:

  • 3 m along the x-axis, and
  • 2 m along the y-axis,

relative to the origin.

Figure 2.3.2 – Position of an object in two dimensions.

Some objects move in three-dimensional space, so three coordinates are required to specify their position.

In three dimensions, position is represented by an ordered triple,

(x,y,z)(x,y,z)

where:

  • x represents the position along the x-axis,
  • y represents the position along the y-axis,
  • z represents the position along the z-axis.

For example, the position (3, 2, 4) means the object is located:

  • 3 m along the x-axis,
  • 2 m along the y-axis,
  • 4 m along the z-axis,

relative to the origin.

Figure 2.3.3 – Position of an object in three dimensions.

Note: The same concept of position applies in one, two, and three dimensions. The only difference is the number of coordinates required to specify the object’s location.

Position Vector

Since position has both magnitude and direction, it is a vector quantity.

The position of an object can therefore be represented by a position vector, usually denoted by

r→\vec{r}

A position vector always starts at the origin and ends at the object’s position.

Figure 2.3.4 – Position vector of an object in two dimensions.

The magnitude of the position vector,

|r→||\vec{r}|

is the straight-line distance between the origin and the object, while its direction indicates the object’s location relative to the origin. The position vector depends on the choice of origin. If the origin changes, the position vector also changes.

Why Is Position Important?

Position tells us where an object is at a particular instant.

If an object’s position changes with time, we can describe its motion using quantities such as distance, displacement, velocity, and acceleration.

The next sections explain the important difference between distance and displacement, both of which are based on changes in position.

Key Points

  • Position describes an object’s location relative to a chosen reference point.
  • The chosen reference point is called the origin.
  • Position can be represented by one, two, or three coordinates.
  • Position is a vector quantity because it has both magnitude and direction.
  • A position vector starts at the origin and ends at the object’s position.
  • The magnitude of a position vector is the straight-line distance from the origin to the object, while its direction indicates the object’s location relative to the origin.
  • The position vector depends on the choice of origin.
  • Changes in position provide the basis for understanding distance and displacement.

← 2.2 Vectors  

2.4 Distance →