# Nakafa Learning Content

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URL: https://nakafa.com/en/subjects/physics/kinematics/reference-frame-position
Source: https://raw.githubusercontent.com/nakafaai/nakafa.com/refs/heads/main/packages/contents/material/lesson/physics/kinematics/reference-frame-position/en.mdx

Learn how to state an object's position using a reference frame, direction sign, and a simple one-dimensional coordinate.

---

## Position Always Asks From Where

If you say, "I am $$30 \text{ m}$$ from the store," your friend can still ask, "which direction?" If you say, "I am east," your friend can still ask, "how far?"

Visible text: If you say, "I am from the store," your friend can still ask, "which direction?" If you say, "I am east," your friend can still ask, "how far?"

In physics, **position** is the location of an object measured from a chosen reference point. That chosen point is called a **reference frame**. A reference frame can be a store, a house, a flagpole, the start line of a race, or the zero point on a coordinate axis.

> A complete position statement names the reference point, value, unit, and direction.

If motion happens along one straight line, we can choose one direction as positive. In the street example, east is positive and west is negative.

```math
x_{\text{relative}}=x_{\text{object}}-x_{\text{reference}}
```

This equation does not move the object. It only changes how we read the object's location from the chosen reference point.

## Position from Different References

Take one object at coordinate $$30 \text{ m}$$ when the store is used as zero. If the reference is changed to Rani's house at coordinate $$20 \text{ m}$$, the object's position becomes $$+10 \text{ m}$$ from Rani.

Visible text: Take one object at coordinate when the store is used as zero. If the reference is changed to Rani's house at coordinate , the object's position becomes from Rani.

The object does not move when the reference point changes. What changes is the way we read the coordinate. If the reference point moves to the right, a large positive position can become a smaller positive position, zero, or even negative.

## Reading Sign and Direction

The sign of a position tells us which side of the reference point the object is on. In the street example, east is chosen as positive. So a positive value means the object is east of the reference point, while a negative value means the object is west of it.

| Reference frame | Object position on the street line | Object relative position |
| :-------------- | :--------------------------------- | :----------------------- |
| Store at $$0 \text{ m}$$ | Object at $$30 \text{ m}$$ | $$+30 \text{ m}$$ east |
| Rani's house at $$20 \text{ m}$$ | Object at $$30 \text{ m}$$ | $$+10 \text{ m}$$ east |
| Naya's house at $$50 \text{ m}$$ | Object at $$30 \text{ m}$$ | $$-20 \text{ m}$$ or $$20 \text{ m}$$ west |

Visible text: | Reference frame | Object position on the street line | Object relative position |
| :-------------- | :--------------------------------- | :----------------------- |
| Store at | Object at | east |
| Rani's house at | Object at | east |
| Naya's house at | Object at | or west |

The value $$-20 \text{ m}$$ does not mean the distance is negative. The negative sign only tells the direction relative to the reference point.

Visible text: The value does not mean the distance is negative. The negative sign only tells the direction relative to the reference point.

## A Position Sentence That Stays Clear

A position sentence needs four parts. If one part is missing, another person can read the object's location from the wrong reference point.

Component: Mermaid
Props:
- title: Building a Position Statement
- description: Follow this order so the object's position is not read from the wrong reference point.
```mermaid
flowchart LR
  A["Observed object"] --> B["Reference frame"]
  B --> C["Value and unit"]
  C --> D["Direction from the reference"]
```

A complete sentence is: "The object is $$10 \text{ m}$$ east of Rani's house." That sentence is clear because it names the object, reference point, distance, unit, and direction.

Visible text: A complete sentence is: "The object is east of Rani's house." That sentence is clear because it names the object, reference point, distance, unit, and direction.

The sentence "the object is near the house" is not enough for physics. Near which house? How many meters? East or west? These small questions matter because kinematics needs positions that can be calculated.

## A Position Sentence from the Store

A marker is at coordinate $$40 \text{ m}$$ from the store. Dimas's house is at coordinate $$30 \text{ m}$$ from the store. If Dimas's house is used as the reference frame, the marker's position is:

Visible text: A marker is at coordinate from the store. Dimas's house is at coordinate from the store. If Dimas's house is used as the reference frame, the marker's position is:

```math
\begin{aligned}
x_{\text{relative}}
&=x_{\text{marker}}-x_{\text{Dimas}} \\
&=40 \text{ m}-30 \text{ m} \\
&=+10 \text{ m}
\end{aligned}
```

So, the marker is $$10 \text{ m}$$ east of Dimas's house. From the store, its position is $$40 \text{ m}$$. From Dimas's house, its position is $$+10 \text{ m}$$. Both statements are correct because they use different reference frames.

Visible text: So, the marker is east of Dimas's house. From the store, its position is . From Dimas's house, its position is . Both statements are correct because they use different reference frames.