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Speed and distance

Free-Standing Mathematics Activity. Speed and distance. How can we model the speed of a car? How will the model show the distance the car travels?. v mph. 70. 0. 2. t hours. Using a graph. Think about How far will it travel in 2 hours?. Car travelling at 70 mph. Area = 2 × 70 = 140.

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Speed and distance

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  1. Free-Standing Mathematics Activity Speed and distance

  2. How can we model the speed of a car? • How will the model show the distance the car travels?

  3. vmph 70 0 2 thours Using a graph Think about How far will it travel in 2 hours? Car travelling at 70 mph Area = 2 × 70 = 140 This is the distance travelled, 140 miles

  4. 20 ms-1 vkph Car accelerating steadily from 0 to 72 kph in 10 seconds =20 metres per second 72 0 tseconds 10 72 kph = Area of triangle = 100 Distance travelled = 100 metres Think about What was the car’s average speed? What is the connection with the graph?

  5. 30 vms-1 18 b a 5 0 tseconds Area = Car accelerating steadily from 18 ms-1 to 30 ms-1 in 5 seconds Area of a trapezium h = 24 × 5 = 120 Distance travelled = 120 metres Think about What was the car’s average speed? What is the connection with the graph?

  6. Car travelling between 2 sets of traffic lights t(s) 0 2 4 6 8 10 12 v(ms-1) 0 5 8 9 8 5 0 v ms-1 9 8 5 C C B B A A 2 4 6 8 10 12 t seconds Think about Why are the strips labelled A, B & C? How will this help to find the area? Area of A = 5 Area of B = 13 Area of C = 17 0 Think about Is this a good estimate? How can it be improved?Is the graph realistic? Total area = 70 Distance travelled = 70 metres

  7. Car travelling with speed v = 0.5t3 – 3t2 + 16 t(s) 0 1 2 3 4 v(ms-1) v 16 13.5 8 2.5 t 0 4 2 3 1 2.5 0 16 13.5 8 Think about What did this car do? Area = = 14.75 + 10.75+ 5.25 + 1.25 Think about How could this estimate be improved? Distance travelled = 32 metres

  8. At the end of the activity • Explain why using triangles and trapezia can only give an estimate of the area under a curve • When is an estimate smaller than the actual value? When is it larger? • How can you improve the estimate? • How well do you think the graphs and functions you have studied model the actual speed of real cars? • In what way would graphs showing actual speeds differ from those used in this activity?

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