KAHIBARO
Table of Contents
What Position Means
Position tells us where an object is located along a chosen line. In one dimensional motion, that line might be a straight road, a hallway, a train track, or the vertical direction up and down. To describe position, we first choose a reference point called the origin, and then measure how far the object is from that point.
If the object is to one side of the origin, its position may be positive. If it is on the other side, its position may be negative. The sign depends entirely on how we choose the direction of the axis.
A common symbol for position is $x$. In vertical motion, people often use $y$ instead, but in one dimensional motion the idea is the same.
Position is not just "how far" something is. Position includes location relative to an origin and includes sign.
Choosing a Coordinate Axis
To describe position clearly, we draw a coordinate axis. This is a straight line with an origin and a positive direction.
For example, suppose a car moves along a straight road. We can place the origin at a traffic light and choose the direction to the right as positive. Then a car 20 meters to the right has position
$$x = 20 \ \text{m}$$
and a car 15 meters to the left has position
$$x = -15 \ \text{m}$$
The same physical place can have different numerical positions if we choose a different origin. This means position depends on the coordinate system we select.
Position as a Number with Units
Position must be given with units. In physics, the SI unit of position is the meter, written as $\text{m}$.
Here are some examples:
| Description | Position |
|---|---|
| Book is 2 meters to the right of the origin | $x = 2\ \text{m}$ |
| Ball is 0.5 meters to the left of the origin | $x = -0.5\ \text{m}$ |
| Person is exactly at the origin | $x = 0$ |
The number tells us the location, and the unit tells us the scale.
Position and Rest
An object is at rest if its position does not change with time. For example, if a chair stays at
$$x = 4\ \text{m}$$
for several seconds, then it is not moving in this one dimensional description.
If its position changes, then the object is moving. The detailed description of how position changes with time belongs to later topics, but the basic idea starts here.
Position Depends on Reference
Position is always measured relative to something. There is no meaningful position without a reference point.
For example, saying "the bus is at 10 meters" is incomplete unless we know 10 meters from where. Once we choose a reference point, the statement becomes meaningful.
This is why two observers can assign different position values to the same object if they use different origins.
A position value has meaning only after a coordinate system and origin have been chosen.
Position and Time
In motion problems, position often changes as time passes. Then position becomes a function of time, written as
$$x(t)$$
This means the position depends on the time $t$. For example, if at different times an object is found at different places, we can record those values in a table.
| Time $t$ (s) | Position $x$ (m) |
|---|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 5 |
This table says that at $t=0$ the object is at $1\ \text{m}$, at $t=1\ \text{s}$ it is at $3\ \text{m}$, and at $t=2\ \text{s}$ it is at $5\ \text{m}$.
We are not yet focusing on speed or velocity here. The key point is that position tells where the object is at each moment.
Reading Position from a Simple Diagram
A one dimensional position axis is often enough to describe many basic situations. For instance, a person walking in a straight corridor can be located by one coordinate only.
In this diagram, one object is to the left of the origin and has a negative position. The other is to the right and has a positive position.
Important Ideas to Remember
Position is one of the most basic quantities in kinematics. It tells where an object is located on a chosen axis. In one dimensional motion, position is represented by a single coordinate such as $x$. The value can be positive, negative, or zero, depending on where the object is relative to the origin.
Key facts about position:
$$x = \text{location relative to an origin along a chosen axis}$$
Position can be positive, negative, or zero.
Position must include units, usually meters.
Position depends on the choice of origin and positive direction.
Once position is known, we can later study how it changes, which leads naturally to displacement, speed, velocity, and acceleration.