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Edexcel International GCSE Physics · Section 1 Forces and motion
4.5.1.1
AQA GCSE Physics · Topic 4.5 Forces · Combined and Triple
Units, Vectors and Scalars
In this lesson you'll learn to: give the unit of every quantity in Forces and Motion,
explain the difference between a scalar (size only) and a vector (size and
direction), and sort any quantity with one question: can it point in different directions?
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Prefer to watch? Scroll to the bottom for the video on this topic
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A video walkthrough is coming soon — it will appear at the bottom of this page
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Start here — have a play
Don't read anything yet. Push the crate in different directions, then turn the block of particles round — which one cares which way it points? Walk from A to B on a wiggly path and watch the distance and the displacement come apart. Then Sort it: finish the unit, decide whether it can point in different directions, and call it a scalar or a vector.
Force: a 20 N push ?
A crate on ice, seen from above. Turn the push, then let go.
20 N towards the east
Press Push!, then turn the arrow and push again. The push is
20 N every time — watch where the crate ends up.
Mass: a block of stuff ?
Mass is how much matter — how many particles — something is made of.
mass = 4.5 kg
Try turning it round. Then try adding or taking away particles.
Which one changes the mass?
The test. Ask one question: can it point in different directions? A push can — east, north, anywhere — and each one does something different, so force is a vector. A lump of stuff cannot point anywhere, so mass is a scalar: a size and nothing else.
Distance travelledscalar
0 m
How far your feet went, along every wiggle. Just a size.
Displacementvector
0 m
The straight line from start to finish — a size and a direction.
Drag B anywhere on the map, then try every route. The distance changes with the route you take; the displacement only cares where you started and where you finished — the shortest straight line between them, and its angle.
right first time 0/0
Finish the unit, then decide
—
1Finish the unit
2Can it point in different directions?
3So it is a…
Pick the unit first.
Your results table — it fills in as you go
| Quantity | Unit | Scalar | Vector |
|---|
Physics With Kate · physicswithkate.com — GCSE & International GCSE Physics
▲ The Sort it tab opens on the ten results from page 3 of your workbook, in the same order.
One question sorts every quantity: can it point in different directions?
If it can, it is a vector. If it can't, it is a scalar. The notes below give you the units, the three pairs examiners love to ask about, and the sentence that gets both marks.
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Revision notes
The units for Forces and Motion
Every answer needs a number and a unit. These are the ones this section uses:
| Quantity | Unit | Say it as |
|---|---|---|
| mass | kg | kilogram |
| distance, displacement | m | metre |
| time | s | second |
| speed, velocity | m/s | metres per second |
| acceleration | m/s² | metres per second squared |
| force, weight | N | newton |
| gravitational field strength, g | N/kg | newtons per kilogram |
| Physics onlymoment of a force | N m | newton metre |
| Physics onlymomentum | kg m/s | kilogram metres per second |
Need the reason a unit is what it is, or how to convert minutes and centimetres first? The Units lesson builds every one of them out of its equation.
Scalars and vectors
Every quantity in physics has a size — physicists call it the magnitude. Some quantities also have a direction, and that splits them into two kinds.
⭐ Learn these two definitions word for word
A scalar quantity has magnitude (size) only — no direction.
A vector quantity has magnitude (size) and a direction.
The quick test: can it point in different directions? A 20 N push can go east, north or anywhere else, and each one does something different — so force is a vector. A 4.5 kg block is 4.5 kg whichever way you turn it, because mass is just how much stuff (how many particles) it is made of — so mass is a scalar.
| Scalars — size only | Vectors — size and direction |
|---|---|
| distance | displacement |
| speed | velocity |
| mass | weight |
| time | acceleration |
| energy, work done | force |
| power | gravitational field strength, g (always downwards) |
| density, temperature | Physics onlymomentum |
| current, potential difference | Physics onlymoment (clockwise or anticlockwise) |
Vectors are drawn as arrows
Because a vector has a direction, we draw it as an arrow. The length of the arrow shows the size, and the way it points shows the direction. That is exactly what a force diagram is: every force on the object, drawn as an arrow.
Distance and displacement
Walk from A to B along a wiggly path. The distance is how far your feet went, wiggles and all — just a length, so it is a scalar. The displacement is the shortest straight line from A to B, in a stated direction — a vector. You give it as a size and an angle or a direction: "260 m at 32° above the horizontal", "15 m north".
⚠ Trap 1 — there and back again
Run once round a 400 m track and finish where you started. Distance = 400 m. Displacement = 0 m, because you ended up back at the start. The displacement can never be bigger than the distance.
Speed and velocity
Speed is how fast — a scalar. Velocity is speed in a stated direction — a vector. Same unit (m/s), different kind of quantity.
⚠ Trap 2 — constant speed, changing velocity
A car going round a roundabout at a steady 10 m/s has a constant speed but a changing velocity, because its direction keeps changing. A change in velocity is an acceleration — so the car is accelerating even though its speed never changes.
Mass and weight
Mass is how much matter something is made of — a scalar, in kg, and the same anywhere in the universe. Weight is the force of gravity on that mass — a vector, in newtons, always pointing down towards the centre of the Earth.
⚠ Trap 3 — a minus sign is not always a direction
For a vector, a minus sign means the opposite direction: if right is positive, a velocity of −5 m/s means 5 m/s to the left. But a temperature of −5 °C just means below zero. Temperature is still a scalar.
How to write it in the exam
The sentence that gets both marks
[quantity] is a [scalar / vector] because it
has [magnitude only / magnitude and direction].
the quantity which kind the reason
State the difference between a scalar and a vector quantity. (2 marks)
A scalar has magnitude (size) only. A vector has magnitude and direction.
Explain why velocity is a vector but speed is not. (2 marks)
Velocity has a magnitude and a direction, so it is a vector. Speed has a magnitude only, so it is a scalar.
A student walks 300 m along a winding path. She ends up 200 m east of where she started. Give her distance and her displacement.
Distance = 300 m (the whole path). Displacement = 200 m east — the straight line from start to finish, with its direction. Writing just "200 m" loses the mark.
Which of these is a vector: mass, time, weight, energy?
Weight. It is a force, measured in newtons, and it always acts downwards. The other three have size only.
✅ Check your answer has both parts
Every "explain" answer here needs 1 the word scalar or vector, and 2 the reason: magnitude only, or magnitude and direction. And every vector you give as an answer needs its direction written next to it.
📘 Now do it in your workbook
Fill in the units table, tick scalar or vector for all twenty quantities, then finish the results table — the same ten you just sorted in the animation.
Define scalars and vectors with six examples of each, measure the walker's displacement, explain the satellite's velocity, then finish the results table — the same ten you just sorted in the animation.
Edexcel iGCSE Forces and Motion Workbook · page 3 AQA GCSE Physics Workbook · FORCES · page 3✅ Can you do it? Tick as you go
0% complete🎉 Nice work! You've ticked off every objective for this spec point.
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Prefer to watch? Here's the whole thing
Video walkthrough — coming soon
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it.
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it. The video is on its way.
🎬
Video coming soon
The walkthrough for this lesson is being filmed and will appear right here. Until then, the notes and the free workbook page above cover every mark.
Now put it into practice
Page 3 of the Forces and Motion workbook is free: twenty quantities to sort and ten results to finish. The full book covers the whole topic with worked answers.
Page 3 of the Forces workbook is free: scalar and vector definitions, the walker's displacement, the satellite's velocity and ten results to finish.
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