Scalars and vectors
The difference between distance and displacement reveals two fundamental groups that every quantity in physics falls into.
Scalar quantities
If stating a magnitude alone is enough to express the value, it is a scalar quantity.
e.g. distance · speed · mass · time
Vector quantities
If a direction is needed as well as a magnitude, it is a vector quantity.
e.g. displacement · velocity · acceleration · weight
Look at them in pairs
These pairs run through the whole chapter. The left column is always the scalar; the right is always the vector.
| Scalar | Matching vector | What the vector adds |
|---|---|---|
| Distance | Displacement | A direction |
| Speed | Velocity | A direction |
A way to tell them apart
If the question "which way?" has to be answered, it is a vector. If it does not, it is a scalar.
"I travelled 5 km" — distance, a scalar. "I travelled 5 km north" — displacement, a vector.