Rates of change

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

Various solids are lowered into a beaker of water. How does the water level rise in each case?

A conveyor belt, with tins placed at regular intervals, is moving at a steady rate towards a labelling machine. A gerbil starts from the beginning of the belt and jumps from tin to tin.

My average speed for a journey was 50 mph, my return average speed of 70 mph. Why wasn't my average speed for the round trip 60mph ?

Match the descriptions of physical processes to these differential equations.

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

Can you find the lap times of the two cyclists travelling at constant speeds?