1.2 Scalars & Vectors

In physics, every measurement is a quantity. We can split all quantities into two groups: scalars and vectors.

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

Speed vs. Velocity

The easiest way to understand this is to compare speed and velocity. Speed is a scalar. If you are running at 5 m/s, your speed is just 5 m/s, no matter which way you are going.

Velocity is a vector. If you are running at 5 m/s East, that is your velocity. If you turn around and run at 5 m/s West, your speed is the same, but your velocity is now completely different.

Because velocity has direction, we often use positive (+) and negative (-) signs. If "East" is positive (+5 m/s), then "West" would be negative (–5 m/s).

Common Examples

• Common Scalars: Distance, Speed, Mass, Time, Energy
• Common Vectors: Displacement, Velocity, Acceleration, Force, Momentum

If all balls in the diagram below are travelling at 5m/s, their speeds are the same. But their velocities are different because they are going in different directions.