Speed and Velocity

Speed tells you how fast something moves. Velocity tells you how fast and in which direction it moves. This difference matters whenever direction changes, like running around a track or taking a U-turn.

Key ideas

• Speed is a scalar (it has size only). Common units: m/s and km/h.
• Velocity is speed in a given direction, so it is a vector (it has size and direction). You can state it with words ("12 m/s north") or signs ("−12 m/s" meaning 12 m/s in the opposite direction).
• Distance is how far you travel along the path. Displacement is the straight-line change from start to finish, with direction.

Equations you need

Average speed:

$$v = \frac{s}{t}$$

where $v$ is speed, $s$ is distance, and $t$ is time.

More generally:

$$\text{average speed} = \frac{\text{total distance travelled}}{\text{total time taken}}$$

Velocity uses the same idea but with displacement and direction.

Units and quick conversions

• 1 m/s = 3.6 km/h
• To change km/h to m/s, divide by 3.6. To change m/s to km/h, multiply by 3.6.

Real-world links

• A car’s speedometer shows instantaneous speed. To state its velocity, you must add direction (e.g., 50 km/h south).
• Moving in a circle at constant speed means velocity is changing, because direction keeps changing.

Common mistakes

• Confusing distance with displacement. They are only the same if you move in a straight line without turning.
• Saying two objects with the same speed have the same velocity. Not true unless their directions match.