GCSE · Physics · Edexcel · Spec 1PH0

Scalar quantities

Your step counter says you walked 8 km today. It doesn't say which way, and it doesn't need to. That's a scalar: it only tells you how much.

Physics · Scalars

How much, or how much and which way?

Pick a quantity, then choose where it belongs. For each one, ask yourself: does it make sense to say which way?

Still to sort

Scalar: size only (0)

A number and a unit tell you everything, like 5 m or 2 kg.

Where the line is: If asking 'which way?' makes no sense, or adds nothing, it belongs here.

Has a direction too (0)

A number and a unit are not enough on their own; it also says which way.

Where the line is: These sound like the scalars next door. The giveaway is the direction: 'north', 'to the left', 'upwards'.

8 of 8 still to sort.

Watch out: Speed and velocity can share the same number. What separates them is whether a direction comes with it.

What a scalar leaves out

ScalarvsVector (its direction-carrying partner)

Read down the rows. Everything on the left follows from one fact: no direction.

Focus

What it tells you

Scalar

How much: the size (magnitude) only

Vector (its direction-carrying partner)

How much, and which way

The insight

This is the whole difference. The scalar isn't 'less accurate'; it just answers a smaller question.

How you write it fully

Scalar

A number and a unit: 5 m, 2 kg

Vector (its direction-carrying partner)

A number, a unit and a direction: 5 m north

The motion pairs

Scalar

Distance and speed

Vector (its direction-carrying partner)

Displacement and velocity

Combining two of them

Scalar

Ordinary arithmetic: 3 m and then 4 m makes 7 m

Vector (its direction-carrying partner)

The directions matter too, so you can't just add the numbers

Predict, then check

Commit to an answer before you reveal it. Your first instinct is worth knowing.

Amira walks 3 m across a room, turns a corner and walks 4 m more. Priya walks 3 m, then carries straight on for another 4 m. Who has walked the greater distance?

Spot the slip

There and back

A dog runs 12 m in a straight line to fetch a ball, then runs 9 m straight back towards where it started. What total distance does the dog run?

A student's answer — which line goes wrong?

The question asks for distance, the total length the dog runs.
First run: 12 m out. Second run: 9 m back.
The second run is in the opposite direction, so it cancels some of the first: 12 m − 9 m = 3 m.
Total distance run = 3 m.

Your turn to write

Put it in your own words

Explain what is meant by a scalar quantity. Give two examples of scalars, and explain how speed is different from velocity. [4 marks]

Your answer

0 words · your answer stays on this page and is not sent anywhere.

The mark scheme

A scalar has size (magnitude) only, with no direction. (1 mark)
Two correct examples, such as mass, time, energy, temperature, distance or speed. (1 mark)
Speed is a scalar: it only says how fast something is going. (1 mark)
Velocity also includes the direction of motion. (1 mark)

Model answer

A scalar quantity has size (magnitude) only; it has no direction, so a number and a unit describe it completely. Mass and time are both scalars. Speed is a scalar: it just tells you how fast something is going, for example 12 m/s. Velocity tells you how fast and in which direction, for example 12 m/s to the west.

Two short phrases carry most of this answer: 'size only' and 'no direction'. Then show the pair: speed is how fast; velocity is how fast and which way.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Some quantities only ever tell you how much. Learn to spot them, see what they leave out, and add them up without tripping over direction.

What you need to know

A scalar quantity has magnitude (size) only. It has no direction.
A number with a unit describes a scalar completely, for example a distance of 5 m or a mass of 2 kg.
Distance, speed, mass, energy, time and temperature are all scalar quantities.
Speed is the scalar partner of velocity, and distance is the scalar partner of displacement. The scalar gives how much, without saying which way.
Scalars add by ordinary arithmetic: walking 3 m and then 4 m covers 7 m, whatever the directions of the two walks.

The big picture

A scalar quantity has size (magnitude) only; it has no direction. A number with a unit describes it completely: 5 m, 2 kg, 30 s. Distance, speed, mass, energy, time and temperature are all scalars. Speed is the scalar partner of velocity, and distance is the scalar partner of displacement: the scalar gives how much, without saying which way. Because direction never comes into it, scalars add by ordinary arithmetic. Walk 3 m and then 4 m and you have covered 7 m, whichever way you turned.

Key points

1The quick test: does it make sense to ask 'which way?' If not, it's a scalar.

2A minus sign on a temperature, such as −5 °C, means below zero. It is not a direction.

3Direction never cancels distance: going there and back still adds up.

4Put scalars in the same unit before you add them.

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Worked example

Problem

A delivery rider makes three trips in a morning: 1.5 km north, then 800 m east, then 2.2 km south. The trips take 6 minutes, 4 minutes and 10 minutes. Find the total distance travelled, in km, and the total time taken.

⚠ Watch out

Treating speed and velocity, or distance and displacement, as two words for the same thing. The scalar only says how much; its partner also says which way. So '20 m/s' is a speed, while '20 m/s north' is a velocity.

🧠

Memory hook

However you twist the route, the distance walked adds up the same. Three steps then four steps is seven steps of walking, every single time.

✓

Check yourself

Without looking back, sort these into scalars and not-scalars: 4 kg, 20 m/s east, 15 s, 300 J, 8 m south. Then say what the two not-scalars include that the scalars don't.

Flashcards

(10)

What is a scalar quantity?

A quantity with magnitude (size) only. It has no direction.

What do you need to describe a scalar completely?

A number and a unit, for example 5 m or 2 kg.

Name six scalar quantities.

Distance, speed, mass, energy, time and temperature.

Speed is the scalar partner of which quantity?

Velocity. Speed says how fast; velocity says how fast and which way.

Distance is the scalar partner of which quantity?

Displacement. Distance says how far; displacement also says which way.

What one question tells you whether a quantity is a scalar?

Does it make sense to say which way? If not, it's a scalar.

How do you add two scalars?

With ordinary arithmetic: put them in the same unit, then add the numbers.

You walk 50 m to a bin and 50 m back. What distance have you walked?

100 m. Coming back doesn't cancel going out.

Does the minus sign in −5 °C make temperature a vector?

No. The minus sign means below zero on the scale, not a direction. Temperature is a scalar.

Is '20 m/s north' a speed or a velocity?

A velocity, because it includes a direction. '20 m/s' on its own is a speed.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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How much, or how much and which way?

There and back

Put it in your own words

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