Speed is the rate at which distance is travelled, whereas velocity is the rate of change of position or displacement. Speed is a scalar quantity; velocity is a vector quantity, so velocity includes direction.
This distinction is part of A.1 Kinematics and applies to both SL and HL students.
Position is measured relative to an origin, so displacement is the change in position. If east is chosen as positive, motion west has negative velocity. Distance adds the length of every part of the path and cannot be negative. Reversing direction therefore changes velocity.
The Key Differences
| Quantity | Speed | Velocity |
|---|---|---|
| Type | Scalar quantity | Vector quantity |
| Definition | Rate of change of distance | Rate of change of position or displacement |
| Direction | Has no direction | Has a specified direction |
| Sign | Normally non-negative | Can be positive, negative, or zero |
| Average value | ||
| SI unit |
Worked Example
A student runs east and then west in a total time of .
The total distance is , so:
The student finishes at the starting position, so the displacement is zero:
This shows that an object can have a non-zero average speed but zero average velocity. At any particular moment, its instantaneous speed is the magnitude of its instantaneous velocity.
After one complete lap of a track, a runner's displacement is zero but distance equals the track length. Average velocity is therefore zero, although average speed is positive.
A common misconception is that negative velocity means an object is slowing down. It does not: a negative velocity only indicates motion in the direction defined as negative. Whether the object is slowing down depends on the directions of both velocity and acceleration.
IB Exam Technique
Before calculating, identify whether the question gives distance or displacement. For velocity, state a direction or use a sign convention; a magnitude without direction may be incomplete when the command term is Calculate or Determine.
