Looking for a Tutor Near You?

Post Learning Requirement »
x

Choose Country Code

x

Direction

x

Ask a Question

x

x
Hire a Tutor
DISCOVER

Numbers

Loading...

Published in: Mathematics
128 Views

Use and apply common measures of rate Solve problems involving average speed

Divya J / Dubai

15 years of teaching experience

Qualification: CAIE and Pearson Examiner for IGCSE an AS Levels, Masters in Mathematics

Teaches: SAT, ACT, Maths, IGCSE/AS/AL, Physics, Biology, Chemistry, Mathematics

Contact this Tutor
  1. Mathematics .- 10 Lecture No Rates Today's Targets Use and apply common measures of rate O Solve problems involving average speed
  2. Compound Measures A compound measure is something that is calculated by using more than one measurement. + Compound measures can be used to measure rates: This measures how much one quantity changes when the other is increased by 1. Examples include: Speed - how much the distance changes for each unit of time. Density - how heavy something is for each unit of its area or volume. Pressure - how much force is applied to an object for each unit of its area. Flow rate - how much the volume changes for each unit of time. Population density - how many people there are for each unit of area.
  3. Compound Measures You can use the formula for a compound measure to derive its units. + Use the units for the quantities in the formula to derive the units of the compound measure. You write a division as a/b or al) -1 and pronounce it as "a per b". Distance Pressur€ Time Force + If the distance is measured in km and the time is measured in mins then the speed is measured in km/min. + If the force is measured in N and the area is measured in cm2 then the pressure is measured in N/cmZ.
  4. Compound Measures You just need to remember what each unit measures. Examples include: kg is a measure of mass and cm3 is a measure of volume. Mass • Therefore Density = • Density can be measured in kg/cm3.
  5. Speed, Density & + Speed, density and pressure are compound measures - they are made from other measures: Speed is related to the measures distance and time. Density is related to mass and volume. Pressure is related to force and area. + The relationship between each of these sets of measures follows the same pattern: Sometimes referred to as "formula triangles". Force Area Pressure
  6. Speed, Density & SPEED, DISTANCE, TIM DENSITY, MASS, VOLUM PRESSURE, FORCE, ARE s
  7. Speed, Density & + Speed is commonly measured in metres per second (m/s) or miles per hour (mph). There are other possibilities such as kilometres per hour (kmph). The units indicate speed is distance per time. i.e., speed = distance + time + "Speed" (in this formula) means "average speed". + In harder problems there are often two journeys - or two parts to one longer journey.
  8. Speed, Density & Pressure + Density is usually measured in grams per cubic centimetre (g/cm3) or kilograms per cubic metre (kg/m3). + The units indicate that density is mass per volume. i.e., density = mass + volume + In harder problems there are often two metals (alloys), liquids or gases that have been combined rather than working with a single substance. You may need to use a volume formula to find the volume of an object first.
  9. Question Liz takes 65 seconds to run 400 m. Calculate her average speed.
  10. Question A train takes 6 hours 39 minutes to travel from New Delhi to Kanpur. The train travels a distance of 429 km. Work out the average speed of the train. Give your answer in km/h correct to one decimal place.
  11. Question A rocket travelled 100 km at an average speed of 28440 km/h. Work out how long it took the rocket to travel the 100 km. Give your answer in seconds, correct to the nearest second.
  12. Question Abelie flew by plane from Dubai to Rome. The flight time was 6 hours 42 minutes. The average speed of the plane was 650 kilometres per hour. Work out the distance the plane flew.
  13. Question Force Pressure = Area Find the pressure exerted by a force of 810 newtons on an area of 120 cm2. 2 Give your answer in newtons /m .
  14. Question Serge walks 7.9 km, correct to the nearest 100 metres. The walk takes 133 minutes, correct to the nearest minute. Calculate the maximum possible average speed of Serge's walk. Give your answer in kilometres/hour.
  15. Question A train of length 105 m takes 11 seconds to pass completely through a station of length 225 m. Calculate the speed of the train in km/h.
  16. Question The distance between Prague and Vienna is 254 kilometres. The local time in Prague is the same as the local time in Vienna. A train leaves Prague at 15:20 and arrives in Vienna at 19:50 the same day. Calculate the average speed of the train.
  17. Question Liquid A has a density of 0.7 g/cm3. Liquid B has a density of 1.6 g/cm3. 140 g of liquid A and 128 g of liquid B are mixed to make liquid C. Work out the density of liquid C.
  18. Question The diagram shows a triangular field, ABC, on horizontal ground. Olav runs from A to B at a constant speed of 4 m/s and then from B to C at a constant speed of 3 m/s. He then runs at a constant speed from C to A. His average speed for the whole journey is 3.6 m/s. Calculate his speed when he runs from C to A. c North
  19. Question (a) Car A and car B take part in a race around a circular track. One lap of the track measures 7.6 km. Car A takes 2 minutes and 40 seconds to complete each lap of the track. Car B takes 2 minutes and 25 seconds to complete each lap of the track. Both cars travel at a constant speed. Calculate the speed of car A. Give your answer in kilometres per hour.
  20. Question (b) Both cars start the race from the same position S, at the same time. (i) Find the time taken when both car A and car B are next at position S at the same time. Give your answer in minutes and seconds. (ii) Find the distance that car A has travelled at this time.
  21. Question A tank is a cuboid measuring 1.8 m by 1.5 m by 1.2 m. Water flows from a pipe into this empty tank at a rate of 200 cm3 per second. Find the time it takes to fill the tank. Give your answer in hours and minutes.
  22. Question A truck is used to transport some wood panels. Each wood panel is a cuboid measuring 2.4 m by 1.2 m by 1.8 cm. The density of each wood panel is 750 kg/m3. The truck can carry 15 tonnes of these wood panels. Calculate the maximum number of wood panels that the truck can carry. Show how you decide. mass The formula for density is
  23. [SIG, 21, Q18] Q. A car of length 4.3 m is travelling at 105 km/h. It passes a bridge of length 36 m. Calculate the time, in seconds, it takes to pass over the bridge completely.
  24. [W17, 41, Ql(c)] Q. Every Monday Sima travels by car to the library. The distance is 20 km and the journey takes 23 minutes. Calculate the average speed for the journey in km/h. (ii) One Monday, she is delayed, and her average speed is reduced to 32 km/h. Calculate the percentage increase in journey time.
  25. [S20, 23, Q4] Q. A train journey takes 5 hours 54 minutes. (a) (b) The journey starts at 09:15. Find the time that the journey ends. The average speed of the train for this journey is 80 km/h. Calculate the distance travelled
  26. [M20, 42, Ql(b)] Q. A train is 61 cm long and travels at a speed of 18 cm/s. It takes 4 second for the whole of the train to cross the bridge. Calculate the length of the bridge.
  27. [W19, 43, Ql(d)] Q. Asif cycles a distance of 105 km. On the first part of his journey he cycles 60 km in 2 hr 24 min. On the second part of his journey he cycles 45 km at 20 km/h. Find his average speed for the whole journey. [41
  28. [W20, 42, QII Q. Karel travelled from London to Johannesburg and then from Johannesburg to Windhoek. (A) The flight from London to Johannesburg took 11 hours 10 minutes. The average speed was 813 km/h. Calculate the distance travelled from London to Johannesburg. Give your answer correct to the nearest 10 km.
  29. [W20, 42, QII Q. Karel travelled from London to Johannesburg and then from Johannesburg to Windhoek. (B) The total time for Karel's journey from London to Windhoek was 15 hours 42 minutes. The total distance travelled from London to Windhoek was 10260 km. Calculate the average speed for this journey. (ii) The cost of Karel's journey from London to Windhoek was $470. (a) [1] (b) [2] Calculate the distance travelled per dollar. Calculate the cost per 100 km of this journey. Give your answer to the nearest cent.

Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Related PPTs

Upload PPTs

If you have your own PowerPoint Presentations which you think can benefit others, please upload on MyPrivateTutor. For each approved PPT you will get 100 Credit Points and 100 Activity Score which will increase your profile visibility.

Upload Now
Home > PowerPoint Slides > Numbers