Number only, or number and direction?

The idea

A complete description of a quantity like displacement needs a direction and a magnitude, its numerical value with units, while total distance travelled needs only its numerical value; the SI unit of both is the metre.

Two statements

"The athlete ran 160 m." "The athlete's displacement is 40 m." One of these statements is complete as it stands. The other needs one more word or sign.

Which one needs more?

• The displacement
• The distance travelled
• Both are equally complete

Is the direction needed?

Tap the box where each quantity belongs.

Magnitude and direction

The numerical value of a quantity with its units is called its magnitude. The total distance travelled needed only a magnitude, such as 160 m. A displacement needed a direction too, such as 40 m in the positive direction.

A complete description of a quantity like displacement needs a direction and a magnitude (its numerical value with units). Total distance travelled needs only its numerical value. The SI unit of both is the metre (m).

Notes

Displacement needs a magnitude and a direction. Total distance travelled needs only a number with units. Both are in metres.

Check yourself

What is the magnitude of a quantity?

Which description of the athlete's motion is complete?

What is the SI unit of distance travelled and of displacement?

Why does total distance travelled not need a direction?

• Its numerical value with units — correct. Yes!
• Its direction. Direction is a separate part of the description. The magnitude is the numerical value with units.
• Its sign only. A plus or minus sign shows the direction. The magnitude is the numerical value with units.
• Displacement: 40 m. Displacement needs a direction too, so this is not complete.
• Displacement: 40 m in the positive direction — correct. Yes!
• Displacement: positive direction. This has a direction but no magnitude, so it is not complete.
• The second. The second is the unit of time, not of distance or displacement.
• The metre per second. Metre per second is the unit of speed and velocity, not of distance or displacement.
• The metre — correct. Yes!
• Only its numerical value (with units) is needed to describe it — correct. Yes!
• Because it is zero. Total distance travelled was 160 m for the athlete, not zero.
• Because it is measured in seconds. It is measured in metres. Seconds measure time.