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Physics · Forces

Distance, displacement, speed and velocity

Distinguish distance and displacement, speed and velocity, recall typical speeds, and use \(s = vt\).

  • 6 key terms
  • All boards
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Warm-up

Answer each one, then check.

  1. 1

    What is the unit of speed?

    Show answerHide answer

    Metres per second (m/s)

  2. 2

    What is speed?

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    How fast something moves

  3. 3

    What is a vector?

    Show answerHide answer

    A quantity with size and direction

  4. 4

    What is a scalar?

    Show answerHide answer

    A quantity with size only

  5. 5

    Convert 2 minutes to seconds.

    Show answerHide answer

    120 s

Learning Objectives

  1. 1Distinguish distance (scalar) from displacement (vector).
  2. 2Distinguish speed from velocity.
  3. 3Recall typical speeds and use a speed = distance ÷ time.
  4. 4Recall and apply \(s = vt\) and calculate average speed.
  5. 5Explain qualitatively that circular motion has constant speed but changing velocity (Higher tier).

SPEED AND VELOCITY

distance travelled \(=\) speed \(\times\) time \(s = vt\)

Distance and speed are scalars. Displacement and velocity are vectors: velocity is speed in a given direction.

Typical Speeds

Learn these values.

  • Walking

    Typical speed (m/s): 1.5

  • Running

    Typical speed (m/s): 3

  • Cycling

    Typical speed (m/s): 6

  • Car

    Typical speed (m/s): 25

  • Train

    Typical speed (m/s): 55

  • Plane

    Typical speed (m/s): 250

  • Sound in air

    Typical speed (m/s): 330

Distance from Speed

A runner travels at 3.0 m/s for 2.0 minutes. How far do they run?

Show the solutionHide the solution
  1. 1 Convert time \(2.0\) min \(= 120\) s
  2. 2 Substitute \(s = vt = 3.0 \times 120\)
  3. 3 Answer \(s = 360\) m

Answer360 m

Average Speed

A cyclist travels 1500 m in 5.0 minutes. Calculate the average speed.

Show the solutionHide the solution
  1. 1 Convert time \(5.0\) min \(= 300\) s
  2. 2 Rearrange \(v = s \div t\)
  3. 3 Answer \(v = 1500 \div 300 = 5.0\) m/s

Answer5.0 m/s

Distance and Displacement

A person walks 3 km east then 4 km north. Find the distance travelled and the displacement.

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  1. 1 Distance \(3 + 4 = 7\) km
  2. 2 Displacement \(\sqrt{3^2 + 4^2} = 5\) km
  3. 3 Direction About 53° north of east

AnswerDistance 7 km; displacement 5 km at 53° north of east.

Circular Motion (Higher)

A car drives round a roundabout at a constant 10 m/s. Explain whether its velocity is constant.

Show the solutionHide the solution
  1. 1 Speed Constant at 10 m/s
  2. 2 Direction The direction of travel keeps changing
  3. 3 Velocity A vector, so a change in direction is a change in velocity

AnswerThe speed is constant but the velocity changes because the direction changes.

Practical Measurement

Measure speed.

  • Measure

    Use a ruler or tape measure for distance and a stopwatch (or light gates) for time.

  • Average speed

    Total distance divided by total time.

  • Non-uniform motion

    Real motion rarely has constant speed, so calculate an average.

  • Variation

    Speed depends on age, terrain, fitness and distance.

Journey Times

A car travels 120 km in 1.5 hours. Calculate its average speed in km/h and in m/s. How long would sound take to travel 660 m?

1. Convert units.

2. Use v = s ÷ t.

A good answer shows: 80 km/h; 80 ÷ 3.6 = 22 m/s. Sound: t = 660 ÷ 330 = 2.0 s.

Can I...?

  1. 1Define distance and displacement.
  2. 2Define speed and velocity.
  3. 3Use \(s = vt\).
  4. 4Calculate average speed.
  5. 5Recall typical speeds.
  6. 6Convert units.
  7. 7Explain circular motion.
  8. 8Give direction for a vector.

Summary & Exam Focus

  • \(s = vt\).
  • Displacement and velocity are vectors.
  • Speed of sound in air about 330 m/s.
  • Circular motion: constant speed, changing velocity.

Exam focus

A runner travels at 3.0 m/s for 120 s. Calculate the distance. (2 marks) (2 marks)

Multiply speed by time.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Distance
How far an object moves; a scalar.
Displacement
Distance in a straight line from start to finish with direction; a vector.
Speed
Distance travelled per unit time; a scalar.
Velocity
Speed in a given direction; a vector.
Average speed
Total distance divided by total time.
Uniform motion
Motion at constant speed in a straight line.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    A runner travels at a steady speed of 3.0 m/s for 120 s. Calculate the distance travelled. Use the equation: distance travelled = speed × time

    Show answerHide answer

    Model answer

    \(3.0 \times 120 = 360\) m

    Mark scheme

    • Correct substitution — 1 mark
    • 360 m — 1 mark
  2. Question 2 Calculate 3 marks

    A cyclist travels 1500 m in 5.0 minutes. Calculate the average speed in m/s.

    Show answerHide answer

    Model answer

    \(t = 300\) s; \(v = 1500 \div 300 = 5.0\) m/s

    Mark scheme

    • Converts to 300 s — 1 mark
    • Correct substitution — 1 mark
    • 5.0 m/s — 1 mark
  3. Question 3 Explain 2 marks

    Explain the difference between distance and displacement.

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    Model answer

    Distance is how far an object moves (a scalar). Displacement is the straight-line distance from the start to the finish in a particular direction (a vector).

    Mark scheme

    • Distance: how far, no direction — 1 mark
    • Displacement: straight line with direction — 1 mark
  4. Question 4 Calculate 3 marks

    A person walks 3 km east and then 4 km north. Calculate (a) the distance travelled (b) the magnitude of the displacement.

    Show answerHide answer

    Model answer

    (a) 7 km. (b) \(\sqrt{3^2 + 4^2} = 5\) km.

    Mark scheme

    • 7 km — 1 mark
    • Pythagoras — 1 mark
    • 5 km — 1 mark
  5. Question 5 Explain 3 marks

    A car travels round a roundabout at a constant speed. Explain why its velocity is changing.

    Show answerHide answer

    Model answer

    Velocity is speed in a given direction. The car's direction keeps changing, so its velocity changes even though the speed is constant.

    Mark scheme

    • Velocity is a vector — 1 mark
    • Direction changes — 1 mark
    • So velocity changes with constant speed — 1 mark

Quick check

  1. Which is a vector?

    1. ASpeed
    2. BDistance
    3. CVelocity
    4. DTime
    Show answerHide answer

    C: Velocity

    It has direction.

  2. A typical walking speed is about...

    1. A15 m/s
    2. B0.15 m/s
    3. C150 m/s
    4. D1.5 m/s
    Show answerHide answer

    D: 1.5 m/s

    About 1.5 m/s.

  3. The speed of sound in air is about...

    1. A330 m/s
    2. B33 m/s
    3. C3 m/s
    4. D3300 m/s
    Show answerHide answer

    A: 330 m/s

    Typical value.

  4. A car at 20 m/s for 10 s travels...

    1. A2 m
    2. B200 m
    3. C30 m
    4. D0.5 m
    Show answerHide answer

    B: 200 m

    20 × 10.

  5. Average speed is...

    1. Atotal time ÷ distance
    2. Bdistance × time
    3. Ctotal distance ÷ total time
    4. Ddisplacement only
    Show answerHide answer

    C: total distance ÷ total time

    Use the whole journey.

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