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

## Problems

### Path to Where?

##### Stage: 1 Challenge Level:

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

### Time Line

##### Stage: 1 Challenge Level:

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

### You Tell the Story

##### Stage: 2 Challenge Level:

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.

### Two Clocks

##### Stage: 2 Challenge Level:

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

### Take Your Dog for a Walk

##### Stage: 2 Challenge Level:

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

### How Far Does it Move?

##### Stage: 3 Challenge Level:

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.

### Decimal Time

##### Stage: 3 Challenge Level:

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

### Speeding Up, Slowing Down

##### Stage: 3 Challenge Level:

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

### Up and Across

##### Stage: 3 Challenge Level:

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.

### Motion Sensor

##### Stage: 4 Challenge Level:

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

### Steady Free Fall

##### 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.