Lesson focus: scalarA quantity that has size but no direction, such as mass or speed. describe size, while vectorA quantity that has both size and direction, such as force or velocity. require both size and direction; this distinction changes how journeys and forces combine.
Classify scalar and vector quantities and calculate simple resultant displacementHow far an object ends up from where it started, in a straight line and in a particular direction. from a described journey.
Build on earlier learning
SpeedYear 8 calculated speed. This lesson separates speed from velocity and distance from displacement.
You will be successful when you can…
- Define scalar and vector.
- Classify common quantities.
- Distinguish distance and displacement.
- Add collinear vectors using signs.
Words that carry the science
- scalar
- A quantity with magnitude but no direction.
- vector
- A quantity with both magnitude and direction.
- magnitude
- The size of a quantity.
- distance
- The total path length travelled; a scalar.
- displacement
- The straight-line change in position in a stated direction; a vector.
- velocity
- Speed in a stated direction; a vector.
Direction changes the quantity
01Direction changes the quantity
Mass, time, distanceHow far something has travelled, measured in metres (m)., speed and energy are scalarA quantity that has size but no direction, such as mass or speed.. displacementHow far an object ends up from where it started, in a straight line and in a particular direction., velocitySpeed in a given direction; it is a vector, so a change of direction is a change of velocity., acceleration, force and weight are vectorA quantity that has both size and direction, such as force or velocity. because their direction affects how they combine.
A value and unit are not always enough for a vectorA quantity that has both size and direction, such as force or velocity.. “5 m s⁻¹ east” is velocity; “5 m s⁻¹” is speed.
02Distance and displacement answer different questions
Distance records the full route. Displacement joins start to finish with a straight line and direction. Returning to the start gives zero displacement even when distance travelled is large.
For one-dimensional motion, choose a positive direction. Motion in the opposite direction receives a negative sign, allowing vectors to add algebraically.
03Vector diagrams communicate scale and direction
A vector arrow points in the quantity’s direction and its length can represent magnitudeThe size of a quantity, such as how big a force is.. Head-to-tail addition shows the resultant from start to finish.
A diagram must state or imply a scale. Decorative arrows that ignore scale can show direction but not support quantitative conclusions.
Force arrows and the resultant force
Forces are vectors: they have a size and a direction. Add them tip to tail to find the resultant force. A zero resultant means the object keeps doing what it was doing; otherwise it speeds up in the direction of the resultant.
Controls
Trolley mass 4 kg, no friction (illustrative). Reset to stop the trolley: balanced forces will not stop it.
Find displacement from a route
A walker travels 120 m east and then 45 m west.
- Choose east as positive.
- Write the vectors as +120 m and −45 m.
- Add them: +120 + (−45) = +75 m.
- Translate the sign back into direction: 75 m east.
How to make the reasoning visible: Distance is 165 m, while displacement is 75 m east.
Compare routes and outcomes
Use east as positive and calculate distance and displacement.
| Journey | Distance / m | Displacement | Quantity type |
|---|---|---|---|
| 30 m east | 30 | 30 m east | distance scalar; displacement vector |
| 30 m east, 10 m west | 40 | 20 m east | different values |
| 20 m east, 20 m west | 40 | 0 m | zero vector |
| 15 m west, 40 m east | 55 | 25 m east | signed addition |
Which journey has zero displacement but non-zero distance?
Why is force a vector?
Check your understanding
Answer from memory, then check against the suggested answer.
What does a vector require?
Is speed scalar or vector?
What is displacement?
A runner completes one 400 m lap. State distance and displacement.
Can an object have constant speed but changing velocity?
Exam Question Practice
Exam Question Practice
Mark points shown after marking
A car travels around a bend at a constant speed.
State the difference between speed and velocity.
(2)Explain why the car is accelerating.
(2)Total for this question: 4 marks
Command word: For explainA command word: say how or why something happens, giving reasons with words like "because" or "so"., link the vector definition of velocity directly to the definition of acceleration.