Speed is how fast something moves. Velocity is how fast and in which direction. That single addition — direction — is the whole difference, and it produces every "trick" question in the chapter.
The comparison table
| Speed | Velocity | |
|---|---|---|
| Definition | Distance travelled per unit time | Displacement per unit time |
| Quantity | Scalar (magnitude only) | Vector (magnitude and direction) |
| Formula | speed = distance / time | velocity = displacement / time |
| Sign | Always positive or zero | Positive, negative or zero |
| Can it be zero while the body moved? | No | Yes — if the body returns to its start |
| Changes when | Magnitude changes | Magnitude or direction changes |
| Unit | m/s | m/s |
Because velocity depends on displacement, and displacement is the straight-line distance from start to finish, average speed ≥ magnitude of average velocity, with equality only for straight-line, one-direction motion.
Example 1 — the round trip
A student walks 300 m to a shop and 300 m back in 10 minutes.
- Distance = 600 m, so average speed = 600/600 s = 1 m/s.
- Displacement = 0 (back where they started), so average velocity = 0.
Not a contradiction: the student moved, but ended up nowhere new.
Example 2 — around a circle
A runner completes one lap of a 400 m track in 80 s.
- Average speed = 400/80 = 5 m/s.
- Average velocity over the full lap = 0 (start = finish).
- Over half a lap (diameter ≈ 127 m, time 40 s), average velocity ≈ 127/40 ≈ 3.2 m/s, while average speed is still 5 m/s.
Example 3 — constant speed, changing velocity
A car goes round a roundabout at a steady 30 km/h. Its speed is constant, but its velocity is changing every moment because its direction is changing — which is why there must be a force (friction) acting on it, and an acceleration toward the centre.
Instantaneous vs average
- Average speed or velocity covers a whole interval (total ÷ total time).
- Instantaneous speed is what the speedometer reads at one moment; instantaneous velocity adds the direction. Mathematically it is the limit as the time interval shrinks to zero — the derivative ds/dt in Class 11.
A common trap: the average of two speeds is not the average speed. Travelling 60 km at 30 km/h and 60 km back at 60 km/h takes 2 h + 1 h = 3 h for 120 km, so the average speed is 40 km/h, not 45.
Uniform and non-uniform
- Uniform velocity: equal displacements in equal intervals — a straight-line graph of position against time.
- Uniform speed does not imply uniform velocity (the roundabout again).
- A body with uniform velocity has zero acceleration; a body with uniform speed may still accelerate.
How examiners ask it
- "Distinguish between speed and velocity" — three rows of the table, scalar/vector first.
- "A body moves in a circle of radius r. Find distance and displacement after half a revolution" — πr and 2r.
- "Can a body have zero velocity and non-zero speed?" — At an instant, no (speed is the magnitude of velocity). On average, yes — the round trip.
- "Give an example of a body with constant speed but changing velocity" — uniform circular motion.