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Kinematics

Kinematics

Speed, distance and time

Unit Conversion Paper 1 + 2 7 min read

On this page
  1. In this note
  2. Formula bank
  3. Speed, distance and time
  4. Average speed over several stages
  5. Ways they test it
  6. Mistakes to avoid
  7. Summary
  8. Practice
  9. Can I do this?
  10. Quiz

In this note

Syllabus 1.12 (average speed) and 2.9
  • 1.12Use speed = distance ÷ time and its rearrangements, with matching units.
  • 1.12Find the average speed of a journey with several stages.
  • 1.12Convert km/h ↔ m/s, and minutes ↔ decimal hours.

Before you start: Time calculations and Rates and unit conversion. Next: Distance-time graphs.

Formula bank

SpeedLearn it\(\text{speed}=\dfrac{\text{distance}}{\text{time}}\)also distance = speed × time, time = distance ÷ speed.Use it when any journey.
Average speedLearn it\(\dfrac{\text{total distance}}{\text{total time}}\)NOT the mean of the speeds.Use it when a journey with stages or a stop.
UnitsLearn itkm/h \(\div3.6\) = m/s; m/s \(\times3.6\) = km/h; minutes \(\div60\) = hoursUse it when mixed units.

Speed, distance and time

Speed is a rate: how much distance is covered per unit of time. The units must match: km with hours gives km/h; metres with seconds gives m/s. Change minutes to hours by dividing by 60 (2 h 30 min = 2.5 h, not 2.3).

General methodHow to answer any speed, distance, time question

  1. Write down what you know and what you want (with units).
  2. Make the units match: time in hours for km/h (minutes ÷ 60), or metres and seconds for m/s.
  3. Choose the formula: s = d ÷ t, d = s × t or t = d ÷ s.
  4. Give the answer with units; turn decimal hours back to hours and minutes if asked.

Example A train leaves at 08 40 and arrives at 11 55, travelling 286 km. Find its average speed.

Time 3 h 15 min = 3.25 h; distance ÷ time.

  1. \(286\div3.25\)

Answer 88 km/h

Try it yourself

1
A car travels 150 km in 2 h 30 min. Speed in km/h?
Show answer

Answer 60

2
How long does 35 km take at 14 km/h? Answer in hours.
Show answer

Answer 2.5

3
Change 72 km/h to m/s.
Show answer

Answer 20

Average speed over several stages

General methodHow to find an average speed

  1. Find the distance AND the time for every stage (use the formula for the missing one).
  2. Add the distances; add the times (include any stops).
  3. Average speed = total distance ÷ total time.

Example A coach travels 120 km at 60 km/h, then 90 km at 30 km/h. Find its average speed.

Find each time, then total ÷ total.

  1. times: \(120\div60=2\) h, \(90\div30=3\) h
  2. total: 210 km in 5 h
  3. \(210\div5\)

Answer 42 km/h (not 45)

Try it yourself

1
Ali walks 4 km at 8 km/h, then cycles for 50 minutes at 18 km/h. Average speed in km/h?
Hint
Walk takes 0.5 h; cycle covers 15 km.
Show answer

Answer 14.25

Ways they test it

Type 1 Speed from clock times

"Leaves 08 40, arrives 11 55, travels 286 km. Average speed?" (2 marks)

Spot it two times of day.

  1. Time taken in hours (3 h 15 min = 3.25 h).
  2. Distance ÷ time.

Type 2 Time in hours and minutes

"How long does 35 km take at 14 km/h? Give your answer in hours and minutes."

Spot it 'hours and minutes'.

  1. t = d ÷ s = 2.5 h.
  2. 0.5 h × 60 = 30 min.

For example \(35\div14=2.5\)

    Answer 2 h 30 min

    Type 3 Several stages

    "120 km at 60 km/h then 90 km at 30 km/h. Average speed?" (3 marks)

    Spot it two or more parts of a journey.

    1. Time for each stage.
    2. Total ÷ total.

    Type 4 Change units

    "A sprinter runs 100 m in 12.5 s. Find the speed in km/h." (2 marks)

    Spot it two different units.

    1. 100 ÷ 12.5 = 8 m/s.
    2. × 3.6.

    For example \(8\times3.6\)

      Answer 28.8 km/h

      Mistakes to avoid

      • ✗ 2 h 30 min = 2.3 h✓ 2.5 hMinutes ÷ 60.
      • ✗ Average of 60 and 30 = 45✓ total ÷ total = 42More time is spent at the slower speed.
      • ✗ Mixing metres and kilometres✓ one unit throughoutUnits must match.

      Summary

      • s = d ÷ t; d = s × t; t = d ÷ s.
      • Average speed = total distance ÷ total time.
      • Minutes ÷ 60 for hours; km/h ÷ 3.6 for m/s.

      If you see …

      • "average speed"total distance ÷ total time, including stops.
      • minutes and km/h togetherchange minutes to hours first.

      Practice

      Practice: easy, medium, hard

      Easy

      1
      45 km in 1 h 30 min. Speed in km/h?
      Show answer

      Answer 30

      2
      Change 15 m/s to km/h.
      Show answer

      Answer 54

      3
      How far do you travel in 3 hours at 42 km/h? (km)
      Show answer

      Answer 126

      Medium

      1
      Sara runs 9 km in 45 minutes. Find her speed in km/h.
      Guide me

      What is it asking? km/h

      What do we know? 45 min = 0.75 h

      Plan 9 ÷ 0.75

      Show working
      1. \(9\div0.75=12\)

      Answer 12

      2
      At 12 km/h, how far does Sara run in 1 h 30 min? (km)
      Guide me

      What is it asking? a distance

      What do we know? 1.5 h

      Plan 12 × 1.5

      Show working
      1. \(12\times1.5=18\)

      Answer 18

      3
      A sprinter runs 100 m in 12.5 s. Speed in km/h?
      Guide me

      What is it asking? km/h

      What do we know? 100 ÷ 12.5 = 8 m/s

      Plan × 3.6

      Show working
      1. \(8\times3.6=28.8\)

      Answer 28.8

      Hard

      1
      A coach travels 120 km at 60 km/h, then 90 km at 30 km/h. Find the average speed (km/h).
      Guide me

      What is it asking? average speed

      What do we know? times 2 h and 3 h

      Plan 210 ÷ 5

      Show working
      1. 2 h + 3 h = 5 h
      2. 210 ÷ 5 = 42

      Answer 42

      PartAnswer / workingMarksGuidance
      times 2 and 3M1
      210 ÷ 5M1
      42A1
      Total: 3 marks
      2
      Ali walks 4 km at 8 km/h, then cycles for 50 minutes at 18 km/h. Find his average speed (km/h).
      Guide me

      What is it asking? average speed

      What do we know? walk 0.5 h; cycle \(18\times\tfrac56=15\) km

      Plan 19 km in \(\tfrac43\) h

      Show working
      1. 19 ÷ 4/3 = 14.25

      Answer 14.25

      PartAnswer / workingMarksGuidance
      0.5 h and 15 kmM1
      \(19\div\tfrac43\)M1
      14.25A1
      Total: 3 marks
      3
      A train leaves at 08 40 and arrives at 11 55, travelling 286 km. Find its average speed (km/h).
      Guide me

      What is it asking? a speed

      What do we know? 3 h 15 min = 3.25 h

      Plan 286 ÷ 3.25

      Show working
      1. \(286\div3.25=88\)

      Answer 88

      PartAnswer / workingMarksGuidance
      3.25 hB1
      88A1
      Total: 2 marks

      Can I do this?

      Anything unticked: revise that section first. All ticked: take the quiz.

      Quiz

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