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MEASUREMENT Derived Units

MEASUREMENT Derived Units. Derived Units or Rates. Derived units come from comparing two quantities with different units (through division) Example: if distance is divided by time we get speed A runner cover 100 metres in 12 seconds. Their average speed is calculated as

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MEASUREMENT Derived Units

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  1. MEASUREMENT • Derived Units

  2. Derived Units or Rates Derived units come from comparing two quantities with different units (through division) Example: if distance is divided by time we get speed A runner cover 100 metres in 12 seconds. Their average speed is calculated as What would their speed be in km/h?

  3. Calculating Units • Kilometres per hour can be written as • Square metres per litre can be written as • Knowing the unit helps with the calculation of the rate • Example • A bar of gold costs $655000, weighs 11.6 kg and has a volume of 600cm3 • Find the cost of gold per gram • Find the weight of gold per cm3 • a) cost per gram has the unit of • b) weight of gold per cm3 has unit

  4. From One Rate to Another Example A killer whale can reach a speed of 15 metres per second. What is this in km/h? 15 metres per second = 60 x 15 metres per minute = 900 = 60 x 60 x 15 metres per hour = 54000 54000 metres per hour = = 54 km/h Or we could write it as

  5. Derived Units Example: calculating the density of lead 10 cubic centimeters has a mass of 113gms How do we calculate the density?  density of lead = = 11.3 g/cm3

  6. Problem Video What average speed (in km/h and also m/s) did Usain Bolt achieve for this race?

  7. Practice A piece of wood measures 1.6m x 50mm x 100mm. It has a mass of 1.3kg. Calculate its density in g/cm3 Wind is blowing at 35km/h. How long will it take for air to travel 400km? Kylie’s car travels 356km using 57L of petrol. What is the consumption rate of fuel? A river flows at a rate of 2.5 km/h. A twig is thrown in upstream. Assuming it is not snagged, how long will it take to travel 6km?

  8. Comparing Prices • When comparing prices it is important to compare the same quantities. • Example • If a 250g (Kingsize) bar of chocolate costs $3.95 • And a 185g (Regular) bar of chocolate costs $2.85 • Which size is the best value for money? • So the ‘rate’ we could compare would be $/kg or c/g (the second option being the easiest) • Therefore the Regular bar of chocolate is better value for money v • Kingsize = • Regular =

  9. Practice Which is better value for money… Cola in a regular 1.5L bottle for $2.75 or Cola in a large 2.25L bottle for $3.60 1 kg block of Edam cheese for $11.59, or a 700g block of Edam cheese for $9.39 90g of toothpaste for $2.25, or 120g of toothpaste for $3.15

  10. Homework Exercise C: Pages 162/163

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