GCSE Physics revision

Distance and displacement

Describing motion along a line

AQA 4.5.6.1.1

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AQA student objectives

Learning pathway

All · Most · Some

ALL 🎯

Distinguish scalar distance from vector displacement, expressing displacement by both magnitude and direction.

MOST 🎯🎯

Apply the specified scientific knowledge of distance and displacement to a relevant example.

SOME 🎯🎯🎯

Analyse an unfamiliar example of distance and displacement using the specified scientific ideas.

Revision summary

Key knowledge

Read on screen, then print for Cornell-style active revision.

Understanding Distance

Distance is the total length of the path actually travelled, regardless of the direction taken.
In the example, the walker followed a winding route through woods, down a road, and up a cliff, covering a total distance of 2,800 metres.
You can measure the distance of a curved or irregular route using a piece of string or the edge of a piece of paper laid along the path on a map.

1. Understanding DistanceAQA

Notes

Distance is the total length of the path actually travelled, regardless of the direction taken.
In the example, the walker followed a winding route through woods, down a road, and up a cliff, covering a total distance of 2,800 metres.
You can measure the distance of a curved or irregular route using a piece of string or the edge of a piece of paper laid along the path on a map.

Understanding Displacement

Displacement is defined as the straight-line distance from the start position to the end position, measured in a specific direction.
In the example, the walker's displacement was approximately 1,400 metres to the northwest, even though the distance travelled was 2,800 metres.
Displacement can be much smaller than distance if the route taken is indirect or winding.

2. Understanding DisplacementAQA

Notes

Displacement is defined as the straight-line distance from the start position to the end position, measured in a specific direction.
In the example, the walker's displacement was approximately 1,400 metres to the northwest, even though the distance travelled was 2,800 metres.
Displacement can be much smaller than distance if the route taken is indirect or winding.

Using Pythagoras' Theorem to Calculate Displacement

When the horizontal and vertical components of a journey are known, Pythagoras' theorem can be used to find the magnitude of the displacement.
If a walker travels 1,000 m west and 1,000 m north, the displacement is calculated as √(1000² + 1000²), giving approximately 1,414 m.
This works because the two components (north and west) form the two shorter sides of a right-angled triangle, with the displacement as the hypotenuse.

3. Using Pythagoras' Theorem to Calculate DisplacementAQA

Notes

When the horizontal and vertical components of a journey are known, Pythagoras' theorem can be used to find the magnitude of the displacement.
If a walker travels 1,000 m west and 1,000 m north, the displacement is calculated as √(1000² + 1000²), giving approximately 1,414 m.
This works because the two components (north and west) form the two shorter sides of a right-angled triangle, with the displacement as the hypotenuse.

Giving Direction to Displacement

A displacement value is incomplete without a direction, which can be expressed as an angle or a compass bearing.
In the example, the diagonal path to the northwest makes a 45° angle, since both the northward and westward components are equal (1,000 m each).
Bearings are measured clockwise from north and range from 0° to 360°, so a northwest direction corresponds to a bearing of 360° - 45° = 315°.

4. Giving Direction to DisplacementAQA

Notes

A displacement value is incomplete without a direction, which can be expressed as an angle or a compass bearing.
In the example, the diagonal path to the northwest makes a 45° angle, since both the northward and westward components are equal (1,000 m each).
Bearings are measured clockwise from north and range from 0° to 360°, so a northwest direction corresponds to a bearing of 360° - 45° = 315°.

Speed and Velocity: The Same Distinction

Speed is a scalar quantity that describes how fast an object is moving, with no reference to direction.
Velocity is a vector quantity that describes speed in a given direction, making it the vector equivalent of speed.
Just as displacement differs from distance, velocity differs from speed by including directional information.

5. Speed and Velocity: The Same DistinctionAQA

Notes

Speed is a scalar quantity that describes how fast an object is moving, with no reference to direction.
Velocity is a vector quantity that describes speed in a given direction, making it the vector equivalent of speed.
Just as displacement differs from distance, velocity differs from speed by including directional information.

Real-World Relevance of Distance vs Displacement

In everyday navigation, the route taken (distance) is often longer than the straight-line path (displacement) due to obstacles such as cliffs, roads, or woodland.
Understanding the difference between distance and displacement is essential in physics when analysing motion, forces, and navigation.
The concept of displacement is particularly important when calculating resultant velocities or when using vector diagrams.

6. Real-World Relevance of Distance vs DisplacementAQA

Notes

In everyday navigation, the route taken (distance) is often longer than the straight-line path (displacement) due to obstacles such as cliffs, roads, or woodland.
Understanding the difference between distance and displacement is essential in physics when analysing motion, forces, and navigation.
The concept of displacement is particularly important when calculating resultant velocities or when using vector diagrams.

Key Equations and Units

Both distance and displacement are measured in metres (m) or kilometres (km) in SI units.
The magnitude of a displacement vector from two perpendicular components a and b is given by √(a² + b²).
Speed is calculated using speed = distance / time, while velocity uses velocity = displacement / time.

Vectors and Diagrams

Vector quantities such as displacement can be represented as arrows on a diagram, where the length shows magnitude and the arrow shows direction.
A right-angled triangle drawn on a grid or map can help visualise the relationship between the horizontal component, vertical component, and the resultant displacement.
A protractor can be used to measure the angle of the displacement vector, helping to determine the precise direction of travel.

8. Vectors and DiagramsAQA

Notes

Vector quantities such as displacement can be represented as arrows on a diagram, where the length shows magnitude and the arrow shows direction.
A right-angled triangle drawn on a grid or map can help visualise the relationship between the horizontal component, vertical component, and the resultant displacement.
A protractor can be used to measure the angle of the displacement vector, helping to determine the precise direction of travel.