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

## Problems

### Motion Sensor

##### Stage: 4 Challenge Level:

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

##### Stage: 4 Challenge Level:

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

### Symmetric Trace

##### Stage: 4 Challenge Level:

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

### Quick Route

##### Stage: 5 Challenge Level:

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

### Out in Space

##### Stage: 5 Challenge Level:

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?

### Towards Maclaurin

##### Stage: 5 Challenge Level:

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.