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© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Model the motion.

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Presentation on theme: "© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Model the motion."— Presentation transcript:

1 © Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Model the motion

2 © Nuffield Foundation 2011 Model the motion What would a velocity–time graph look like for each of these? How can we model motion? Are there any connections between the graphs? What would a displacement–time graph look like?

3 © Nuffield Foundation 2011 t (s) x (m) 0 10 2030 60 120 180 30 90 150 Sprinter runs at 9 ms -1 for 10 seconds, stops for 10 seconds, then runs at 9 ms -1 for another 10 seconds in the same direction. 0 10 20 3 6 9 30 v (ms -1 ) t (s) Gradient = xx tt xx tt = 9 The gradient of the displacement–time graph gives the velocity Area under the velocity–time graph gives the displacement Area = 10  9 = 90 Think about: What would a velocity–time graph look like? Think about: What would a displacement–time graph look like?

4 © Nuffield Foundation 2011 Sprinter runs at 9 ms -1 for 10 seconds, stops for 10 seconds, then takes 10 seconds to run back to his starting point. 0 10 20 – 3 3 9 30 v (ms -1 ) 6 – 6 – 9 t (s) Gradient = 9 ms -1 The gradient of the displacement–time graph gives the velocity Area under the velocity–time graph gives the displacement Area = 90 m Area = –90 m Gradient = –9 ms -1 t (s) x (m) 0 10 20 30 60 90 30 xx tt xx tt Total = 0 Think about: What would a velocity-time graph and a displacement- time graph look like?

5 © Nuffield Foundation 2011 t (s) x (m) 0 4 8 12 2610 200 100 A mechanic drives a car at a steady speed of 20 ms -1 for 8 seconds then puts on the brakes to come to a halt 4 seconds later. The gradient of the displacement–time graph gives the velocity Area under the velocity–time graph gives the displacement 10 20 v (ms -1 ) t (s) 0 4 8 12 2610 = 40 m = 20 ms -1 Area A = 160 m A Area B B Gradient B varies from 20 to 0 ms -1 B Gradient A A Think about: What would a velocity–time graph and a displacement–time graph look like this time?

6 © Nuffield Foundation 2011 A driver drives her car 1.2 km to a garage, spends 8 minutes checking her tyres then drives the car back home again. 0 10 v (ms -1 ) 5 – 5 – 10 t (min) 4 8 12 2610 = 10 ms -1 Gradient gives the velocity Area gives the displacement Area = 10  120 Area = – 10  120 Gradient = – 10 ms -1 x (m) 0 21012468 400 800 1200 200 600 1000 t (min) xx tt xx tt Gradient = 1200 m = – 1200 m Think about: Can you sketch a displacement-time graph? Think about: Can you sketch a velocity-time graph?

7 © Nuffield Foundation 2011 The distance between two bus stops is 60 metres. A bus sets off from the first bus stop and reaches a speed of 10 ms -1 before braking to stop at the second bus stop. Gradient gives the velocity Area gives the displacement t (s) v (ms -1 ) 0 4 8 12 2610 5 t (s) x (m) 20 40 60 10 30 50 0 4 8 12 2 6 10 = 40 m = 20 m Area A A Area B B Gradient A varies from 0 to 10 ms -1 A Gradient B varies from 10 to 0 ms -1 B Think about: Can you sketch a velocity-time graph? Think about: What is the displacement in each part? Think about: What does the displacement-time graph look like?

8 © Nuffield Foundation 2011 A remote controlled car reverses 10 metres then travels 30 metres forward at the same speed. This takes a total of 20 seconds. Gradient gives the velocity Area gives the displacement x (m) 0 10 20 – 10 15 20 5 t (s) 10 0 1 2 v (ms -1 ) – 1 – 2 t (s) 15 20 5 10 = 2 ms -1 Area = 2  15 Area = – 2  5 Gradient = –2 ms -1 xx tt xx tt Gradient = 30 m = –10 m Total = 20 m Think about: What would a displacement- time graph and a velocity-time graph look like this time?

9 © Nuffield Foundation 2011 Model the motion Reflect on your work Is speed the same as velocity? What is the difference between distance and displacement? How realistic are the graphs as models of the motion described? How are velocity–time graphs and displacement–time graphs related? What would more realistic graphs look like?


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