Question

Q6: What is the difference between speed and velocity?

Answer 1

Speed and velocity both measure how fast something moves, but they differ in one crucial way: direction.

- Definition
- Speed: a scalar quantity — how fast an object is moving (no direction). Always nonnegative.
- Velocity: a vector quantity — how fast and in what direction the object is moving.

- Formulas
- Average speed = total distance traveled / total time.
- Average velocity = displacement / total time (displacement is a vector from start to finish).
- Instantaneous velocity = dx/dt (and instantaneous speed = |v|, the magnitude of velocity).

- Key differences
- Direction: speed has none; velocity includes direction.
- Sign: speed ≥ 0; velocity can be positive, negative, or zero depending on chosen axis.
- Distance vs displacement: speed uses total distance; velocity uses displacement.
- Motion examples: in uniform circular motion speed can be constant while velocity changes continuously (direction changes). If you go out 5 km east and 5 km back west in 2 hours, average speed = (10 km)/2 h = 5 km/h, but average velocity = (0 km)/2 h = 0 km/h.

- Units: same units (m/s, km/h, etc.), but interpreted differently because velocity carries direction.

Summary: speed tells how fast; velocity tells how fast and which way.