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Vectors and scalars: displacement and velocity

A scalar quantity has size (magnitude) only. A vector quantity has both magnitude and direction. Distance and speed are scalars. Displacement and velocity are vectors.

Distance is the total length of the path travelled, whatever direction it goes in. Displacement is the straight-line distance from the start to the finish, in a stated direction. A student who walks 6 m north and then 6 m south has travelled a distance of 12 m but has a displacement of 0 m, because they finish where they started.

Speed is how fast an object moves, with no direction. Velocity is speed in a stated direction, found from displacement divided by time. Two cars at 20 m/s in opposite directions have the same speed but different velocities. A runner who completes one lap of a 200 m track has travelled 200 m, but the displacement and so the average velocity are zero. Velocity also changes when direction changes, even if the speed stays constant.

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