Speed vs Velocity

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 dfrac518)

Data table

Velocity (signed)
Time (s)	Speed / velocity (m s⁻¹)
0	4
3	4
4	0
7	-2

Speed (= |velocity|)
Time (s)	Speed / velocity (m s⁻¹)
0	4
3	4
4	0
7	2

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)

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.

Scroll diagram horizontally to read all labels.

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

Example 1: Average speed (straight line)Core

A boy runs a distance of 100 m in 11.32 s. Find his average speed.

Show Answer

Use average speed = total distance / total time:

average speed = 100 m/11.32 s

average speed = 8.83 m s⁻¹

Example 2: Average speed vs average velocity (U-turn)Core

A car travels 5 km due east, then makes a U-turn and travels 3 km back. The journey takes 0.30 h.

Find:

1. distance travelled
2. displacement
3. average speed
4. average velocity

Show Answer

1. Distance travelled: 5 km + 3 km = 8 km

2. Displacement (east is positive): 5 km-3 km = 2 km east

3. Average speed: 8 km/0.30 h = 26.7 km h⁻¹

4. Average velocity: 2 km/0.30 h = 6.67 km h⁻¹ east

Example 3: Constant speed on a curved pathCore

A cyclist rides round a circular track at constant speed.

1. Is the cyclist’s speed constant?
2. Is the cyclist’s velocity constant? Explain.

Show Answer

1. Yes. Speed is constant because its value (magnitude) does not change.
2. No. Velocity is not constant because the direction of motion changes continuously, so the velocity changes even if speed stays the same.

Example 4: Unit conversionCore

Convert 90 km h⁻¹ to m s⁻¹.

Show Answer

90 km h⁻¹ = 90/3.6 m s⁻¹ = 25.0 m s⁻¹

Example 5: Average speed vs average velocity (right-angle path)Core

A student walks 60 m east, then 80 m north in 70 s.

Find:

1. average speed
2. magnitude and direction of average velocity

Show Answer

Distance travelled:

distance = 60 + 80 = 140 m

Average speed:

average speed = 140/70 = 2.0 m s⁻¹

Displacement magnitude:

|Δ s| = sqrt60² + 80² = 100 m

Average velocity magnitude:

|average velocity| = 100/70 = 1.43 m s⁻¹

Direction:

tanθ = 80/60 Rightarrow θ ≈ 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.

8. Practice, Quiz and Next Step

Close your notes and use Speed vs Velocity in the supplied context below. This requires a constructed explanation or working, not recognition of an option.

Fresh context: A runner completes one 400 m lap in 80 s and stops at the starting point.

1. Retrieve: define speed, velocity and direction in your own words, including units, sign or conditions where relevant.
2. Represent: Draw the closed path and the zero displacement vector from start to finish.
3. Apply: Calculate average speed and average velocity and explain why one is non-zero while the other is zero.

Check the response before looking back

• Scalar and vector quantities are distinguished, including direction and sign.
• A graph result is inferred from its labelled axes before a formula is chosen.
• Working uses compatible units and the final statement describes the motion.

If one check fails, name that exact gap, revisit the matching explanation or worked example, and redo the task with different values or a different situation. Then use theO-Level topic checks orpractice browser for an independent re-test.