Chapter 2, titled "Non-Linear Relations", is about discovering and describing non-linear patterns in the behavior of physical objects.
On pages 15 and 15R students figure out how to use the ticker-tape data that they collected in the falling body experiment to create a graph of displacement vs. time. On pages 15c and 17c are special exercises for use with ultrasonic motion recorders, if they are available. On pages 16 and17 students figure out how to create an equation to describe that parabolic graph. Students should begin work on their Ch. 2 Review Sheet immediately. pages 18 and 18R give students some practice in creating equations to fit data. Examples include the ideal gas law, the pendulum's period vs. length, and the gravitation law. On page 19 students discover some neat tricks for solving proportion problems. On pages 20 and 20R students use the new proportion methods to discover the easy way to estimate the relative uncertainty of a product. On pages 21 and 22 students generalize their discoveries about percent changes in non-linear relations to discover a very powerful tool. On pages 23 and 24 students investigate the motion of an object sliding to a stop on a smooth, level surface. More modern methods for recording motion can be introduced here if they are available. On pages 25 and 26 students practice solving simpler motion problems. The distinction between speed and velocity is introduced here. On pages 24b and 25b students practice solving more interesting acceleration problems. On page 27 we develop a general procedure for solving any motion problem. On pages 26b and 27b the expansion of the universe and other non-trivial motion problems are explored. On pages 28 and 28b we develop a procedure for transforming a speed-time graph into the corresponding displacement-time graph. The distinction between average and instantaneous acceleration is developed on p. 28b. On pages 29 and 28b we define "tangent lines" and use that idea to clarify instantaneous speed and acceleration. On 29b students who are ready for it can discover the fundamental theorem of calculus. On pages 31b and 32b present more interesting motion problems for review. (These pages can be given to well-motivated students at a later time, after Chapter 3 has been started.)