Scientists often make measurements. The physical quantities they measure fall into two categories: scalars and vectors. Scalar and vector quantities are treated differently in calculations.

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Vector quantities have size or magnitude as well as an associated **direction**. This makes them different from scalar quantities, which only have a size or magnitude.

Some examples of vector quantities that refer to motion include:

- displacement, eg 50 kilometres (50 km) east
- velocity, eg 11 metres per second (11 m/s) upwards

Notice how the quantities above have both a **size** and a **direction** associated with them.

The direction of a vector can be given in a written description, or drawn as an arrow. The length of an arrow represents the magnitude of the quantity.

Displacement is the overall distance from a fixed point. Average velocity is the total displacement divided by time.

If an athlete runs 400 m north before turning back and running 400 m south at the same speed, their overall displacement is 0 m. Although the athlete has run 800 m in total, their final distance from the starting point is 0 m as they have returned to the start.

The average velocity of the athlete is also 0 m/s, due to the fact that their displacement is 0 m. If the athlete runs at a velocity of *v* m/s in one direction, then their velocity in the opposite direction must be -*v* m/s. These two values cancel each other out, giving 0 m/s overall.