GCSE · Physics · Edexcel · Spec 1PH0

Difference between vector and scalar

A runner runs one full 400 m lap and stops exactly where she began. She has run 400 m. She has also gone nowhere. How can both be true?

Physics · Scalars and vectors

Scalar or vector? You decide.

Pick a quantity, then pick its box. Don't peek: commit first.

Still to sort

Scalar (0)

Size (magnitude) only, no direction.

Where the line is: The size is the whole answer. Distance, not displacement. Speed, not velocity.

Vector (0)

Size and direction.

Where the line is: The answer needs a size and a direction. Displacement, not distance. Velocity, not speed.

11 of 11 still to sort.

Eleven quantities, two boxes. Commit first, then read why.

Exam line: Ask one question of every quantity: does it need a direction as well as a size?
Watch out: Distance and displacement, speed and velocity: they look like twins, but only one of each pair has a direction.

Back to our runner

She runs one full 400 m lap and stops on the start line.

What are her distance travelled and her displacement?

Physics · Speed and velocity

Same speed, different velocity

East is positive. Slide each car's tag to its velocity in m/s.

Vectors are drawn as arrows

Scalars simply add: 5 kg + 5 kg = 10 kg. Tap each arrow to see what happens when two vectors pull against each other.

box

Tap a force to see what it does.

Physics · Direction matters

Where does Sam's answer go wrong?

Sam walks 30 m north along a straight path, then turns round and walks 10 m back south. Sam is asked for the displacement from the start.

Sam's answer — which line goes wrong?

Exam line: Write a vector as a size and a direction, every time.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

  • A scalar has size (magnitude) only. A vector has size and direction.
  • Scalars: speed, distance, mass, energy, time, power. Vectors: displacement, velocity, force, acceleration, momentum.
  • Have a goYour friend Priya is confidently sure that power is a vector. Scalar or vector, and is Priya right?

    Power is a scalar, so Priya is wrong.

    Power is on the scalar list: it has a size and no direction goes with it.

  • Distance is how far you've travelled along your path, whatever the direction. That makes it a scalar.
  • Displacement is the straight-line distance from the start, plus the direction from start to finish. That makes it a vector.
  • Run one full 400 m lap and your distance is 400 m, but your displacement is zero.
  • Speed is a scalar. Velocity is speed in a particular direction, so it's a vector.
  • Have a goA satnav says 'you are travelling at 30 m/s' and never says which way. Is that a speed or a velocity?

    A speed.

    30 m/s is a size only. It would only become a velocity if it also gave a direction.

  • Two cars each moving at 6 m/s in opposite directions have the same speed but different velocities.
  • On a straight line, choose one direction as positive and the opposite as negative: +6 m/s and −6 m/s.
  • Have a goWest is positive. A skateboard rolls east at 2 m/s. Write its velocity with a sign.

    −2 m/s

    East is opposite to the positive direction, so it gets the minus sign. The speed is still 2 m/s.

  • Write down a vector and you must give its size and its direction, or the answer is incomplete.
  • Combining vectors means taking direction into account, so a resultant can be smaller than the sum of the sizes.

The big picture

A scalar has size only; a vector has size and direction. That one extra ingredient is why a runner can cover 400 m yet have zero displacement, why two cars at 6 m/s can have different velocities, and why vectors need their direction written down and taken into account when they combine.

Key points

1Direction is the whole difference: a scalar has size only, a vector has size and direction.
2Distance and speed are scalars. Their vector partners, displacement and velocity, carry a direction.
3A full lap gives a distance of 400 m but a displacement of zero.
4Equal speeds in opposite directions mean different velocities, shown on a straight line as + and −.
5A vector answer always needs its size and its direction.

Worked example

Problem

A hiker walks 5 km east along a straight track, then turns round and walks 3 km west along the same track. Find the distance she has walked and her displacement from the start, and say which of the two is a vector.

⚠ Watch out

Treating distance and displacement, or speed and velocity, as the same thing with two names. The vector partner always carries a direction: a full lap is 400 m of distance but zero displacement, and two cars at 6 m/s in opposite directions share a speed but not a velocity.

🧠

Memory hook

A scalar says how much. A vector says how much and which way.

✓

Check yourself

Cover the page. A friend says 'distance and displacement are just two words for the same thing.' Using one lap of a running track, explain why they're wrong.

Flashcards

(13)
What is the difference between a scalar and a vector?
A scalar has magnitude (size) only. A vector has magnitude and direction.
Name six scalar quantities.
Speed, distance, mass, energy, time and power.
Name five vector quantities.
Displacement, velocity, force, acceleration and momentum.
Distance: scalar or vector, and what does it measure?
A scalar. It measures how far you've gone along your path, whatever the direction.
What is displacement?
The straight-line distance from the starting point, together with the direction from start to finish. It's a vector.
What is the displacement of a runner who finishes a full lap back at the start?
Zero. The straight-line distance from the start is zero, however far she ran.
How are speed and velocity related?
Speed is a scalar. Velocity is speed in a particular direction, which makes it a vector.
Two cars each move at 6 m/s in opposite directions. What is the same and what is different?
The speed is the same. The velocities are different, because the directions are different.
How can a straight-line vector's direction be shown with a sign?
Choose one direction as positive and the opposite as negative, e.g. +6 m/s and −6 m/s.
What must you include when you write down a vector?
Both its magnitude and its direction. Without the direction, the answer is incomplete.
How do scalars combine, in contrast to vectors?
Scalars simply add (5 kg + 5 kg = 10 kg). Vectors must be combined with their directions taken into account.
Can the resultant of two vectors be smaller than the sum of their sizes?
Yes. When directions are taken into account, vectors that act against each other partly cancel.
How are vectors commonly shown on diagrams?
As arrows.

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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