Distance, Time, Velocity and Rates of Change - March 2006, Stage 4&5

Problems

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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.