*Student Reading Page:* Position
and Distance

Look at the picture below. When
you ask, “Where is the camera?” you are asking for the position of the object.
Very often position may be defined in terms of its *distance* from other
objects, hence the confusion.

A person might describe the picture above thus: “The camera is 5 cm to the right of the sink. The plant is 12 cm to the right of the sink.” These statements imply that if the zero mark of a ruler were at the sink, the camera is 5 cm to the right and the plant is12 cm to the right.

What happens when an object moves? We use the same terminology.

**Example
1**: In the picture below the camera has moved so that it is 8 cm from the
sink. How much did its position change?

To keep things straight, we define the starting and ending positions of the
objects: the starting or initial position is defined as *x _{i}* = 5 cm. The ending or final
position is defined as

*D**x* = final position – initial
position

*D**x = x _{f} –x_{i }*

*D**x* = 8 – 5 = 3 cm.

Camera end position Camera start position

**Example
2**: The camera starts at 6 cm and moves so that it is 2 cm from the sink.
How much did its position change?

Here* x _{i}*
= 6 cm, and

*D**x *= 2 – 6 = -4 cm.

Since we define position as having increasing values toward the right, the negative value of Dx indicates that the camera has moved to the left.

What is distance?

The distance along a straight line is the difference between the position
readings – however, distance is defined as a positive quantity. Whether the
object moves to the left or the right, the distance is always positive, while
its change in position can be positive or negative. The distance does not
contain information about the direction, while the change in position does.

Mathematically, we write distance as the magnitude (also called the amount or absolute value) of the change in position. This is indicated by the standard mathematical symbols.

In example 1, the distance the camera moves is |*D**x*| = |8 – 5| = 3 cm.

In example 2, the distance the camera moves is |*D**x*| = |2 – 6| = |-4| = 4 cm.

The **change in position** is the difference between the
final and initial position readings:_{}.

The **distance** along a
straight line is the magnitude (or amount) of the change in position *|**D**x| = |x _{f}
–x*

Distance is frequently used to figure out how far apart two objects are.

**Example 3**: the distance between the camera and the
plant is *|**D**x|
=*12 – 5 = 8 cm.

**Example 4**: (scale in km).

The distance between the school bus and the plane is *|**D**x| =*
4 – (-6) = 10 km

Positions are frequently defined by placing objects on a graph, where the “zero” is a convenient reference point.

_{}for
initial or starting position

_{}for final
or ending position

_{}for change
in position

(Note that the change in position can be a positive or a negative value)

_{}for
distance

(Note that distance is the absolute value of change in position)

In a later activity we will use similar symbols for clock readings:

_{} for initial
or starting clock reading

_{} for final
or ending clock reading

_{} for the
time interval