EX: How does the yeast population change with time? How well do your data support the idea that the yeast population obeys a logistic model?

EX: How does the speed of a pendulum change with clock time? How does the maximum speed change with pullback? How does restoring force change with position?

EX: What is the force vs. stretch behavior of a rubber band? At what point does the rubber band permanently change its shape?

EX: How does the frequency of a hanging piece of #9 steel wire change with its length? (note that the same sort of analysis can be used to tune chimes cut from conduit)

EX: How does the charge on a capacitor discharging through a voltmeter change with time? How does the voltage of a generator change with cranking rate? How does the force on a conductor in a magnetic field change with current? How does the strength of a magnet change with distance?

EX: How does the paper helicopter behave when its various physical parameters are changed?

EX: What cools a cup of hot coffee better, adding ice right away or near the end? Why? Quantify the entire process, including the relevant differential equations.

EX: Using a string and some washers prove that when something drops it speeds up.

EX: Using a string and some washers investigate the relationship between the distance an object drops and the time required for it to drop. From your data investigate the relationship between the position of the object and its velocity, using the ideas of rates and/or sequences S, S’ and S’’ (S being the sequence of the positions of the falling object taken at uniform time intervals).

EX: If a series of bottles each contains a strong salt solution, and if the bottles are connected by thin tubing so that salt can diffuse from one bottle to another, are the results consistent with the predictions of a bugs-on-trees model?

EX: How does the intensity of a light beam vary with the distance it travels through a homogeneous material? What sort of model might help make sense of your intensity vs. distance function?

EX: How is the angular distance of rotation of a beam on a low-friction support related to the time required to move that distance? What do your results tell you about average rates of change of position, and about average rates of change of velocity?

EX: How is the distance rolled by a cart down a constant incline related to the time required to move that distance? What do your results tell you about average rates of change of position, and about average rates of change of velocity?

EX: If an object whose temperature differs from that of the room in which it is placed is observed over a period of time, what happens to the temperature? What does a graph of temperature vs. clock time look like? What sort of function best fits the data? Is it true that the rate at which temperature changes is directly proportional to the difference between the temperature of the object and that of the room? Why should it be so?

EX/NP: How does the water resistance on an object vary with the speed of the object? This is very relevant to swimmers and the associated question: If you had a videotape of a swimmer pushing hard off a wall, how could you determine from the sequence S of swimmer positions taken at intervals of .01 second the water resistance being encountered, and is there a limit to how hard the swimmer should push in terms of time saved vs. energy required?

EX/NP/CE: How is the force on a bead in a beads-and-string model related to the S’’ sequence of the bead configuration? If the rate at which the velocity of the bead changes is proportional to the force on it, then how does this affect changes in the S’ sequence? How does this then allow us to update the S sequence? What does this have to do with wave motion? How can we program this process? How could we use Excel to model this process?

NP/CE: How can we use a cellular automaton to mimic wave behavior?

NP/EX: If water flows from one cylinder into another identical cylinder, both with fixed holes of the same size, where the water in the first cylinder is deeper than that in the second, how does depth change with respect to clock time in the second cylinder? What would be the depth vs. clock time in a third cylinder?