Distance, Time, Velocity and Rates of Change - March 2006, All Stages

Problems

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Path to Where?

Stage: 1 Challenge Level: Challenge Level:1

Can you imagine where I could have walked for my path to look like this?

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Time Line

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Describe what Emma might be doing from these pictures of clocks which show important times in her day.

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You Tell the Story

Stage: 2 Challenge Level: Challenge Level:1

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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Two Clocks

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

These clocks have only one hand, but can you work out what time they are showing from the information?

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Take Your Dog for a Walk

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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How Far Does it Move?

Stage: 3 Challenge Level: Challenge Level:1

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

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Decimal Time

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Use the clocks to investigate French decimal time in this problem. Can you see how this time system worked?

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Speeding Up, Slowing Down

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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Up and Across

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

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Motion Sensor

Stage: 4 Challenge Level: Challenge Level:1

Looking at the graph - when was the person moving fastest? Slowest?

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Steady Free Fall

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you adjust the curve so the bead drops with near constant vertical velocity?

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Symmetric Trace

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Points off a rolling wheel make traces. What makes those traces have symmetry?

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Quick Route

Stage: 5 Challenge Level: Challenge Level:1

What is the quickest route across a ploughed field when your speed around the edge is greater?

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Out in Space

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

A space craft is ten thousand kilometres from the centre of the Earth moving away at 10 km per second. At what distance will it have half that speed?

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Towards Maclaurin

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.