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Speed vs Velocity

Key idea: Understand speed vs velocity (scalar vs vector), including direction, sign conventions, unit conversions, and exam-style worked examples for O Level Physics.

  • SEC G3 Physics 2027
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Learning objectives

  • State what speed means
  • State what velocity means, including its direction
  • Calculate average speed from total distance and total time
  • Calculate acceleration as change in velocity divided by time taken
  • State what uniform acceleration means
  • Interpret examples of non-uniform acceleration
  • Plot and interpret displacement–time and velocity–time graphs in one dimension
  • Deduce rest and uniform or non-uniform velocity from a displacement–time graph
  • Deduce rest, uniform velocity and uniform or non-uniform acceleration from a velocity–time graph
  • Use signed area under a velocity–time graph to determine displacement
  • Recall constant free-fall acceleration near Earth as approximately 10 m/s²

1. Definition

A. Speed

Speed is the rate of change of distance travelled with time. It is a scalar (no direction).

B. Velocity

Velocity is the rate of change of displacement with time. It is a vector (magnitude + direction).

2. Key Ideas

  • Speed uses distance; velocity uses displacement (see Distance vs Displacement).
  • Average speed:
    • average speed = total distance travelled / total time taken
  • Average velocity:
    • average velocity = total displacement / total time taken, with direction
  • Instantaneous speed is the speed at an instant (measured by a speedometer).
  • Constant speed does not guarantee constant velocity (direction might change).
  • SI unit for both is m s⁻¹.
  • Common conversion:
    • 1 m s⁻¹ = 3.6 km h⁻¹
    • km h^-1 → m s^-1: divide by 3.6 (same as 5/18)

Velocity can be negative; speed cannot

Two lines compare signed velocity (which can be negative when direction reverses) with speed, which is always the magnitude of velocity and never negative.

Scroll across the graph to read all labels.

Two lines compare signed velocity (which can be negative when direction reverses) with speed, which is always the magnitude of velocity and never negative.Two lines compare signed velocity (which can be negative when direction reverses) with speed, which is always the magnitude of velocity and never negative.
When direction reverses, velocity changes sign. Speed is a scalar, so it is always ≥ 0.
Open full-size graph
View figure data
Values for Velocity can be negative; speed cannot
Time (s)Velocity (signed)Speed (= |velocity|)
044
344
400
7-22

3. Detailed Explanations

A. Prerequisite: distance vs displacement

  • Distance travelled: total path length (scalar).
  • Displacement: straight-line change from start to end, with direction (vector).

If this is unclear, revise first: Distance vs Displacement.

B. Speed vs velocity (comparison table)

FeatureSpeedVelocity
Usesdistance travelleddisplacement
Typescalarvector
Direction needed?noyes
Can be negative?noyes (depends on chosen direction)
SI unitm s⁻¹m s⁻¹
“Constant” meanssame valuesame value and same direction

C. Instantaneous vs average

Instantaneous speed is what the speed is right now. A car speedometer displays this magnitude; it does not give the car’s direction, so it does not display velocity.

Average speed and average velocity are calculated over a time interval:

  • A car can have an average speed of 60 km h⁻¹ over a trip even if the speedometer does not read 60 km h⁻¹ all the time.

D. Constant speed vs constant velocity

  • Constant speed: the speed stays the same, but direction may change.
  • Constant velocity: both speed and direction stay the same.

Example: A runner moving around a circular track at constant speed has changing velocity because the direction keeps changing.

Constant speed with changing velocityA runner moves anticlockwise around a circular track. Equal-length velocity arrows at the right and top point in different tangent directions, showing equal speed but changing velocity.Same speed, different directionsABv at Av at BWhat stays constant?Arrow length → speedWhat changes?Arrow direction → velocity
Scroll diagram horizontally to read all labels.
Equal arrow lengths show constant speed. The tangent direction changes around the track, so velocity changes.

E. Positive and negative velocity (1D)

In one-dimensional motion, you must choose a positive direction (e.g. “to the right is positive”):

  • moving right: positive velocity
  • moving left: negative velocity

4. Common Mistakes

A. Concept mistakes

  • Writing a velocity without direction (e.g. “5 m s⁻¹” instead of “5 m s⁻¹ east”).
  • Saying “speed is constant so velocity is constant” (false if direction changes).
  • Using distance when the question asks for displacement (or vice versa).

B. Calculation mistakes

  • Mixing km h⁻¹ and m s⁻¹ without converting.
  • Using average speed formula when asked for average velocity (or vice versa).
  • Forgetting to convert minutes/hours into seconds when using SI units.

5. Exam Tips

A. How to write for full marks

  • For calculations:
    • write the equation
    • substitute values with units
    • compute
    • final answer with unit (and direction for velocity)
  • For explanation questions:
    • always mention “velocity changes if direction changes” (even when speed is constant)

6. Worked Examples

Modelled example 1

Average speed (straight line)

Core

Problem

A boy runs 100 m in 11.32 s. Find his average speed.
Study the worked solution

  1. Choose total distance over total time

    Method

    Use the average-speed relationship.

    Reason

    Speed is based on path length and does not require a direction.

    Working

    average speed = 100/11.32 = 8.83 m s⁻¹

Guided practice 2

Average speed vs average velocity (U-turn)

About 6 min

Problem

A car travels 5 km east, then 3 km west in 0.30 h. Find distance, displacement, average speed and average velocity.

Separate path length from directed change

Unit: km
Unit: km
Unit: km h^-1
Unit: km h^-1

Hints

Hint 1: separate the numerators
Distance adds path lengths; displacement keeps direction.
Hint 2: divide by the common time
Use distance for average speed and displacement for average velocity.
View solution step by step

  1. Find distance and displacement

    Method

    Add magnitudes for distance and combine directions for displacement.

    Reason

    The U-turn reverses direction but does not erase travelled path.

    Working

    d = 5 + 3 = 8 km, Δ s = 5-3 = 2 km east

  2. Calculate the two averages

    Reason

    Both rates use the same total journey time but different numerators.

    Working

    v bar _speed = 8/0.30 = 26.7 km h⁻¹, vector v bar = 2/0.30 = 6.67 km h⁻¹ east

Common misconception 3

Constant speed on a curved path

Find and correct the mistake

Learner response

A cyclist rides around a circular track at constant speed. A student says the velocity is therefore constant. Locate the error.

Check both parts of velocity

Which property changes?

View solution step by step

  1. Distinguish scalar and vector conditions

    Method

    Keep speed constant but track direction.

    Reason

    Velocity is constant only when both magnitude and direction remain unchanged.

    Working

    The cyclist’s speed is constant, but the tangent direction changes continuously, so velocity changes.

Examiner practice 4

Unit conversion

2 marks

Examination question

Convert 90 km h⁻¹ to m s⁻¹. [2 marks]

Show the conversion factor

View solution step by step

  1. Apply the conversion factor

    1 mark

    Method

    Divide kilometres per hour by 3.6.

    Reason

    1 km = 1000 m and 1 h = 3600 s.

    Working

    90÷3.6

  2. State the converted speed

    1 mark

    Reason

    The requested SI velocity unit is metres per second.

    Working

    90 km h⁻¹ = 25.0 m s⁻¹

Challenge 5

Average speed vs average velocity (right-angle path)

Minimal support

Two-dimensional transfer

A student walks 60 m east, then 80 m north in 70 s. Find average speed and the magnitude and direction of average velocity.

Use path length and vector displacement separately

Unit: m s^-1
Unit: m s^-1
Unit: degrees

Hints

Hint 1: find two different lengths
Distance is 60 + 80; displacement is the hypotenuse of a right triangle.
Hint 2: find direction
Use tan θ = 80/60 measured north of east.
View solution step by step

  1. Calculate average speed

    Method

    Divide total path length by time.

    Reason

    Speed uses distance travelled.

    Working

    v bar _speed = (60 + 80)/70 = 2.0 m s⁻¹

  2. Find the displacement vector

    Method

    Combine perpendicular components.

    Reason

    Average velocity uses the straight-line change in position.

    Working

    |Δ s| = square root of (60² + 80²) = 100 m, θ = tan⁻¹ (80/60) ≈ 53°

  3. Calculate average velocity

    Reason

    Divide displacement by the same total time and include direction.

    Working

    | vector v bar| = 100/70 = 1.43 m s⁻¹, 53° north of east

7. Mind Stretchers

Mind stretcher 1: Can instantaneous velocity be negative if average velocity is positive?Extension

A particle moves left for a short time, then moves right and ends far to the right of its starting point. Its average velocity over the whole trip is positive.

Can its instantaneous velocity have been negative at some time? Explain.

Show Answer

Yes. While the particle is moving left, its instantaneous velocity is negative. The average velocity can still be positive if the final displacement is in the positive direction.

Mind stretcher 2: If average velocity is non-zero, must instantaneous velocity always be non-zero?Extension

If an object’s average velocity over a time interval is non-zero, does that mean its instantaneous velocity is never zero during the interval?

Show Answer

No. The object can stop temporarily (instantaneous velocity = 0) and still have a non-zero average velocity if the final displacement over the whole interval is non-zero.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027