Velocity and Speed: What Is the Difference?

Speed is the distance travelled per unit time. Velocity is speed in a stated direction. This distinction is a common source of lost marks, especially for Extended candidates.

Why does direction matter?

Speed is a scalar (magnitude only). Velocity is a vector (magnitude and direction). Two cars travelling at 20 m/s in opposite directions have the same speed but different velocities.

This matters in three situations that appear regularly on IGCSE papers:

1. Displacement calculations. A ball thrown upward at 15 m/s has a velocity of +15 m/s (upward). When it falls back, its velocity becomes −15 m/s (downward). Its speed is still 15 m/s.
2. Circular motion. A satellite orbiting at constant speed has a continuously changing velocity because its direction changes. This changing velocity means it is accelerating.
3. Combining velocities. A boat crossing a river has a velocity affected by both its engine and the current. These velocities add as vectors, not scalars.

How is velocity defined formally?

$\text{velocity} = \frac{\text{displacement}}{\text{time}}$

Displacement is the straight-line distance from start to finish in a specified direction. A runner who completes a full lap of a 400 m track in 50 s has a speed of 8 m/s but a velocity of 0 m/s (displacement is zero).

Common errors and how to correct them

• Defining velocity as “how fast something moves”. This is the definition of speed. Velocity must include a reference to direction: “displacement per unit time” or “speed in a given direction.”
• Saying constant speed means constant velocity. Not true for curved paths. An object moving in a circle at constant speed has a changing velocity.
• Using speed and velocity interchangeably in written answers. Examiners distinguish them. Use the correct term for the context.

How to apply this in an exam

When a question asks you to “state what is meant by velocity”, write: speed in a stated direction (or displacement per unit time). If asked whether a quantity is a scalar or vector, remember that velocity is a vector and speed is a scalar.