Speed vs Velocity
Speed asks how fast. Velocity asks how fast and in which direction. That single extra word changes the calculation, because velocity is built on displacement rather than on the distance actually travelled.
Scalar and vector
- Speed is a scalar: a size only, and never negative.
- Velocity is a vector: a size and a direction.
- Average speed is total distance over time.
- Average velocity is displacement over time, where displacement is the straight line from start to finish.
Distance versus displacement
Distance is how far you actually travelled along your path. Displacement is how far you ended up from where you started, in a straight line, with direction. Walk a full lap of a track and the distance is 400 m while the displacement is zero.
Why it matters for acceleration
Acceleration is the rate of change of velocity, not of speed. A car going round a bend at a steady 60 km/h has constant speed and changing velocity, because its direction is changing. That makes it accelerating, which is the point the question is usually testing.
Worked examples
Example 1
Question
A runner completes one lap of a 400 m track in 80 s. Find the average speed and the average velocity.
Answer
Average speed 5 m/s, average velocity 0
Steps
- 1Average speed uses distance travelled: 400 / 80 = 5 m/s.
- 2Displacement is the straight line from start to finish.
- 3The runner finished where they started, so the displacement is 0 m.
- 4Average velocity = 0 / 80 = 0 m/s.
- 5The runner clearly moved, but they did not end up anywhere else.
This is the standard exam question on the topic. A zero average velocity with a non-zero average speed is the giveaway that the path returned to its start.
Example 2
Question
A walker goes 3 km east, then 4 km north, taking 2 hours. Find average speed and average velocity.
Answer
Average speed 3.5 km/h, average velocity 2.5 km/h north-east
Steps
- 1Total distance: 3 + 4 = 7 km, so average speed = 7 / 2 = 3.5 km/h.
- 2Displacement is the straight line from start to finish, found with Pythagoras.
- 3Displacement magnitude = root of (3^2 + 4^2) = root 25 = 5 km.
- 4Average velocity = 5 / 2 = 2.5 km/h, in the direction of that straight line.
- 5A velocity answer without a direction is incomplete.
Example 3
Question
A car drives round a roundabout at a constant 30 km/h. Is it accelerating?
Answer
Yes
Steps
- 1Its speed is constant, so a speed-based answer would say no.
- 2Acceleration is the rate of change of velocity, and velocity includes direction.
- 3Going round a bend continuously changes the direction of travel.
- 4So the velocity is changing even though the speed is not.
- 5Therefore the car is accelerating, and the force causing it points towards the centre of the circle.
Common mistakes
Using total distance to calculate velocity.
Velocity uses displacement. If the path is not a straight line, the two are different numbers.
Giving a velocity with no direction.
A vector answer needs a direction, whether as a compass bearing, an angle, or a sign.
Saying constant speed means no acceleration.
Only if the direction is also constant. Circular motion at constant speed is accelerating.
Treating a negative velocity as a mistake.
It means motion in the negative direction you defined, which is a normal, correct answer.
Practice it
Work these out first, then open the answer. Stuck halfway? Select the problem and ask Solvecoon for the step you are missing.
1. A sprinter runs 100 m in a straight line in 10 s. Find average speed and average velocity.
Show answer
Both are 10 m/s, because the path is a straight line, so distance equals displacement.
2. You cycle 5 km to school and 5 km home in 1 hour total. What is your average velocity?
Show answer
Zero. The displacement is zero because you ended where you began, even though the average speed is 10 km/h.
3. A ball is thrown up and caught at the same height. Over the whole flight, what is its average velocity?
Show answer
Zero, for the same reason: the displacement over the round trip is zero.
Questions people ask
- Can speed be negative?
- No. Speed is a magnitude, so it is zero or positive. Velocity can be negative, meaning the opposite direction.
- Is instantaneous speed the same as instantaneous velocity?
- Their magnitudes are equal at any instant. The velocity also carries the direction of travel at that instant.
- Which one does a car speedometer show?
- Speed. It has no idea which way you are pointing, which is exactly what makes it a scalar instrument.
- How do I find displacement from a path with turns?
- Treat the legs as vectors and combine them. For a right-angled path, that is Pythagoras plus an angle.
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