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By the end of this topic, you should be able to:
In physics, every measurement we make falls into one of two categories: scalars or vectors.
Scalar quantities have magnitude only. Magnitude simply means size or amount. When you measure a scalar, you only need to state how much of it there is. For example, if someone asks "How far did you walk?", you might say "5 kilometres". That's all the information needed – just the distance.
Vector quantities have both magnitude and direction. When you measure a vector, you need to state both how much of it there is AND which way it's pointing. For example, if someone asks "What is your displacement?", you need to say something like "5 kilometres north-east". The direction matters just as much as the distance.
Here's a simple way to tell if something is a vector or scalar: Can two equal amounts cancel each other out?
Let's look at the most important example to understand this concept:
Distance is the total length of the path you actually travelled. It doesn't matter which direction you went – you just add up all the metres or kilometres you covered. Distance is a scalar.
Displacement is the straight-line distance from your starting point to your finishing point, measured in a specific direction. It's like drawing an arrow directly from start to finish. Displacement is a vector.
Example: Imagine walkers who travel from town A to town B (8 km), then from town B to town C (7 km). Their winding route means they covered a total distance of 15 km. However, if you draw a straight line from town A to town C, it's only 10 km. Their displacement is 10 km in the direction from A to C (let's say 30° east of north).
You need to know which quantities are scalars and which are vectors:
Scalar quantities (magnitude only):
Vector quantities (magnitude and direction):
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