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Vector and scalar quantities

Physical quantities fall into two types. A scalar quantity has magnitude (size) only. A vector quantity has both magnitude and direction. To describe a vector fully you must say how big it is and which way it points.

Scalar quantities include distance, speed, mass, time, energy and temperature. Vector quantities include force, weight, displacement, velocity and acceleration. Several quantities come as a pair. Distance is a scalar and displacement is a vector: displacement is the straight-line distance from the start to the end, in a stated direction. Speed is a scalar and velocity is a vector: velocity is speed in a stated direction.

The difference matters in calculations. A student walks 3 m east and then 3 m west. The distance travelled is 6 m, because distances simply add up. The displacement is 0 m, because the student finishes back at the start. A car travelling at 20 m/s has a speed of 20 m/s, and its velocity is 20 m/s north only once the direction is given. A car going round a bend at steady speed has a changing velocity because its direction changes.

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