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Teach GCSE Maths Speed

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Speed © Christine Crisp "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

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Suppose we travel 80 km in 1 hour. If I travel the next 40 km in 1 hour my average speed for this 2 nd hour is halved to 40 km per hour. However, from the information that we travelled 80 km in 1 hour, we can find the average speed. At times we could be travelling very fast and at others we might have stopped at traffic lights. Sometimes we will be accelerating and sometimes slowing down. The average speed is 80 km per hour. The average speed for the journey is 60 km per hour.

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If we draw a graph of distance and time, the average speed is given by how steep the line is. We can use a graph to find the average speed. 80 km 1 hour 40 km 1 hour 80 km/h 40 km/h 1 st hour: 80 km 2 nd hour: 40 km average speed = distance time

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average speed = distance time We can use this formula to find either: speed if we know distance and time, or Write d, s, and t in alphabetical order in a warning triangle. d s t Tip: A way to remember this formula: distance if we know speed and time, or time if we know distance and speed.

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average speed = distance time Write d, s, and t in alphabetical order in a warning triangle. d s t Tip: A way to remember this formula: Tip: Check the letters are in the right order by noting the units for speed. e.g. km/h, kilometres over hours. d t We can use this formula to find either: speed if we know distance and time, or distance if we know speed and time, or time if we know distance and speed.

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For time cover up the t.For distance cover up the d. distance is speed time For speed cover up the s. average speed = distance time We can use this formula to find either: speed if we know distance and time, or Write d, s, and t in alphabetical order in a warning triangle. d s t The triangle gives d over t (distance over time). Tip: A way to remember this formula: distance if we know speed and time, or time if we know distance and speed. time is distance over speed. speed is distance over time.

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e.g.2Find the time taken, in minutes, to travel 30 miles at an average speed of 40 mph ( miles per hour ). d s t time = distance speed time = Solution: hour = 0·75 hour Since the distance is in miles and the speed in mph, the time is in hours. We will have to change it to minutes. Tell your partner how many minutes are in 0·75 ( or three quarters ) of an hour. Ans: 45 mins If we dont recognise the answer, to change from hours to minutes we multiply by 60.

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e.g.3Without using a calculator, find the distance travelled on a trip that takes 20 minutes if the average speed is 6 km/h. Solution: Without a calculator, if we have mixed units...

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e.g.3Without using a calculator, find the distance travelled on a trip that takes 20 minutes if the average speed is 6 km/h. Solution: Without a calculator, if we have mixed units... it is often easier not to use the formula. A speed of 6 km/h means 6 km travelled in 1 hour ( or 60 minutes ). This is 1 km in 10 minutes or 2 km in 20 minutes. The answer is 2 km.

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SUMMARY d s t average speed = distance time We can use a warning triangle to find the formula that links average speed, distance and time. letters in alphabetical order, time = distance speed distance = speed time If the units for speed are km/h, the units for distance must be km and for time must be hours. Non-calculator problems are usually easier without the formula.

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EXERCISE 1.Find the average speed if a car travels a distance of 220 km in 4 hours. 2.Find the distance walked in three and a half hours at an average speed of 2 mph. 4.Without using a calculator, find the average speed for a journey of 10 miles in 15 minutes. Give your answer in miles per hour. 3.Find the time taken to run 5 km at an average speed of 8 km/h. Give your answer in minutes.

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EXERCISE 1.Find the average speed if a car travels a distance of 220 km in 4 hours. 2.Find the distance walked in three and a half hours at an average speed of 2 mph. Solution: d s t average speed = distance time = 55 km/hour = d s t distance = speed time = 2 3·5 = 7 miles Solution:

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EXERCISE 3.Find the time taken to run 5 km at an average speed of 8 km/h. Give your answer in minutes. d s t = 0·625 hours 5 8 = = 0· minutes = 37·5 minutes Solution: time = distance speed

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EXERCISE 4.Without using a calculator, find the average speed for a journey of 10 miles in 15 minutes. Give your answer in miles per hour. Solution: We have the distance travelled in 15 minutes. 20 miles in 30 minutes 40 miles in 60 minutes Doubling the numbers: Doubling again: The average speed is 40 mph. We need to find the distance travelled in 1 hour ( 60 minutes ). 10 miles in 15 minutes

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