Nuffield FreeStanding Mathematics Activity Model the motion Nuffield

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

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

Model the motion How can we model motion? What would a velocity–time graph look

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

Sprinter runs at 9 ms-1 for 10 seconds, stops for 10 seconds, then runs

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. Think about: What would a x (m) velocity–time graph look like? v (ms-1) 9 180 150 6 x 120 90 3 t 60 x 30 0 10 20 30 t (s) Area = 10 9 = 90 Area under the velocity–time graph gives the displacement © Nuffield Foundation 2011 0 t 10 20 30 t (s) Think about: Gradient = What would a = 9 displacement–time graph look like? The gradient of the displacement–time graph gives the velocity

Sprinter runs at 9 ms-1 for 10 seconds, stops for 10 seconds, then takes

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

A mechanic drives a car at a steady speed of 20 ms-1 for 8

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. x (m) v (ms-1) 200 20 10 B 100 A A B 0 2 4 6 8 10 12 0 t (s) Area under the velocity–time graph gives the displacement Area A = 160 m Area B © Nuffield Foundation 2011 = 40 m 2 4 6 8 10 12 t (s) The gradient of the displacement–time graph gives the velocity Think. Gradient about: A = 20 ms-1 What would a velocity–time graph and a Gradient B varies from 20 like to 0 this ms-1 time? displacement–time graph look

A driver drives her car 1. 2 km to a garage, spends 8 minutes

A driver drives her car 1. 2 km to a garage, spends 8 minutes checking her tyres then drives the car back home again. Think about: Can you sketch a displacementv (ms-1) time graph? x (m) 1200 10 1000 5 800 x x 600 0 400 200 0 t (min) 2 4 6 8 10 12 – 5 t t 2 4 6 8 10 12 t (min) Gradient gives the velocity Gradient = 10 ms-1 © Nuffield Foundation 2011 Gradient = – 10 ms-1 – 10 Area the displacement Thinkgives about: Can you sketch a velocity-time graph? Area = 10 120 = 1200 m Area = – 10 120 = – 1200 m

The distance between two bus stops is 60 metres. A bus sets off from

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. v (ms-1) Think about: x (m) Can you sketch 60 a velocity-time graph? 10 B 50 Think about: 40 What is the displacement in each part? 30 5 A B A 20 10 0 2 4 6 8 10 12 Area gives the displacement Area A © Nuffield Foundation 2011 Area B = 40 m = 20 m t (s) 0 2 4 6 8 10 12 t (s) Gradient gives the velocity Think about: What does the from displacement-time Gradient A varies 0 to 10 ms-1 graph look like? -1 Gradient B varies from 10 to 0 ms

A remote controlled car reverses 10 metres then travels 30 metres forward at the

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

Model the motion Reflect on your work What is the difference between distance and

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