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Compound Measures

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Notes de leçon

Compound Measures Overview

  • A compound measure uses more than one measurement (e.g., speed = distance ÷ time).
  • Compound measures often describe rates – how one quantity changes per unit of another.
  • Examples: speed, density, pressure, flow rate, population density, fuel consumption.
  • Units are derived from the formula, e.g., km/h means distance (km) per time (h).
  • Use formula triangles to rearrange: cover the variable you need, then multiply or divide the other two.

Speed, Distance & Time

  • Speed = distance ÷ time (average speed over a journey).
  • Common units: m/s or km/h.
  • Distance = speed × time; Time = distance ÷ speed.
  • Check units: if distance is in km and time in minutes, speed is km/min.
  • For mixed units (e.g., minutes and hours), convert to consistent units before calculating.
  • In multi‑part journeys, treat each part separately or combine total distance and total time.

Speed, Distance, Time Formula Triangle

Speed, Distance, Time Formula Triangle

Density, Mass & Volume

  • Density = mass ÷ volume.
  • Common units: g/cm³ or kg/m³.
  • Mass = density × volume; Volume = mass ÷ density.
  • An object floats if its density is less than the density of water (1 g/cm³).
  • Ensure consistent units: convert kg to g or m to cm as needed.

Density, Mass, Volume Formula Triangle

Density, Mass, Volume Formula Triangle

Pressure, Force & Area

  • Pressure = force ÷ area.
  • Common units: N/m² (also called Pascals, Pa).
  • Force = pressure × area; Area = force ÷ pressure.
  • Remember: weight is a force (measured in newtons), not mass.
  • Area units must match: if force is in N and area in m², pressure is N/m².

Pressure, Force, Area Formula Triangle

Pressure, Force, Area Formula Triangle

Unit Conversions

  • Always check if the answer requires different units (e.g., m/s to km/h).
  • To convert km/h to m/s: multiply by 1000/3600 (or divide by 3.6).
  • To convert m/s to km/h: multiply by 3600/1000 (or multiply by 3.6).
  • For time: 1 hour = 60 minutes = 3600 seconds.
  • For mass: 1 kg = 1000 g; for length: 1 km = 1000 m; for volume: 1 m³ = 1 000 000 cm³.

Worked Examples – Speed

  • Example: George drives 315 km in 3 h 30 min. Average speed = 315 ÷ 3.5 = 90 km/h.
  • Example: A speedboat travels 84 km/h. Convert to m/min: 84 × 1000 ÷ 60 = 1400 m/min.
  • Example: Ivan walks 1.5 km in 20 min. Speed = 1.5 ÷ (20/60) = 4.5 km/h.
  • Example: A car travels at 20 m/s for 10 km. Time = 10 000 ÷ 20 = 500 s = 8 min 20 s.

Worked Examples – Density & Pressure

  • Density example: Wood block 8 × 20 × 10 cm, mass 1360 g. Volume = 1600 cm³, density = 1360/1600 = 0.85 g/cm³ (floats).
  • Pressure example: Force 300 N on area 5 m². Pressure = 300/5 = 60 N/m².
  • Pressure example: Force 300 N, pressure 0.6 N/cm², width 20 cm. Area = 300/0.6 = 500 cm², length = 500/20 = 25 cm.
  • Always state units in final answer.

Exam Tips

  • Memorise the three formulas: speed, density, pressure.
  • Watch for mixed units (e.g., minutes and hours) – convert before calculating.
  • Use formula triangles to avoid rearranging errors.
  • Show all working clearly, especially when converting units.
  • For floating questions, compare density to water (1 g/cm³).

Diapos

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  1. 1.A car travels 180 km in 3 hours. What is its average speed in km/h?

    Easy
    • A60 km/h
    • B540 km/h
    • C30 km/h
    • D90 km/h

  2. 2.What is the formula for pressure?

    Easy
    • AP = F / A
    • BP = F × A
    • CP = A / F
    • DP = F + A

  3. 3.A substance has a mass of 50 g and a volume of 25 cm³. What is its density?

    Easy
    • A2 g/cm³
    • B0.5 g/cm³
    • C1250 g/cm³
    • D75 g/cm³

  4. 4.A force of 200 N is applied over an area of 4 m². What is the pressure?

    Easy
    • A50 N/m²
    • B800 N/m²
    • C0.02 N/m²
    • D200 N/m²

  5. 5.George drives 315 km in 3 hours 30 minutes. What is his average speed in km/h?

    Medium
    • A90 km/h
    • B105 km/h
    • C80 km/h
    • D110.25 km/h

  6. 6.A speedboat travels at 84 km/h. Convert this speed into metres per minute.

    Medium
    • A1400 m/min
    • B5040 m/min
    • C1.4 m/min
    • D84000 m/min

  7. 7.Ivan walks 1.5 km in 20 minutes. What is his average speed in km/h?

    Medium
    • A4.5 km/h
    • B3 km/h
    • C0.075 km/h
    • D30 km/h

  8. 8.A cuboid block of wood measures 8 cm × 20 cm × 10 cm and has mass 1360 g. The density of water is 1 g/cm³. Will the block float?

    Hard
    • AYes, because its density is 0.85 g/cm³
    • BNo, because its density is 1.18 g/cm³
    • CYes, because its density is 1 g/cm³
    • DNo, because its density is 0.85 g/cm³

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