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Vectors and scalars: distance, displacement, speed and velocity

A scalar quantity has only a size (magnitude). A vector quantity has both a magnitude and a direction.

Distance and speed are scalars. Distance is the total length of the path travelled, whatever the route. Displacement and velocity are vectors. Displacement is the straight-line distance from the start point to the finish point, in a stated direction. Velocity is speed in a stated direction.

Suppose a student walks 40 m north, turns round and walks 40 m south back to the start. The distance travelled is 80 m, but the displacement is 0 m because she finished where she began.

Direction matters, so a vector can be positive or negative. If east is positive, a velocity of 5 m/s west is written as -5 m/s. An object moving round a circle at constant speed has a changing velocity, because its direction keeps changing.

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