1.  State the definition of rate of change.

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2.  State the definition of velocity.

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3.  State the definition of acceleration.

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4.  A ball rolls along a path, moving from position 20 cm to position 50 cm as its velocity increases from 5 cm/s to 15 cm/s.

• What is its change in velocity and how do you obtain it from the given information?  &&&&
• What is its change in position and how do you obtain it from the given information?  &&&&

5.  A ball accelerates from velocity 30 cm/s to velocity 80 cm/s during a time interval lasting 10 seconds.  Its v vs. t graph is a straight line (i.e., acceleration is uniform).

Explain in detail how to use the definitions you gave above, along with the linearity of the v vs. t graph, to reason out

• the average velocity of the ball during this interval, &&&&

and

• its acceleration during this interval.  &&&&

Remember, the main goal is to use a detailed reasoning process which connects the given information to the two requested results.  You should use units with every quantity that has units, units should be included at every step of the calculation, and the algebraic details of the units calculations should be explained.

6.  A ‘graph trapezoid’ has ‘graph altitudes’ of 40 cm/s and 10 cm/s, and its base is 6 seconds.  Explain in detail how to find each of the following:

• The rise of the graph trapezoid.  &&&&
• The run of the graph trapezoid.  &&&&
• The slope associated with the trapezoid.  &&&&
• The dimensions of the equal-area rectangle associated with the trapezoid.  &&&&
• The area of the trapezoid. &&&&

Each calculation should include the units at every step, and the algebraic details of the units calculations should be explained.

7.  If the altitudes of a ‘graph trapezoid’ represent the initial and final positions of a ball rolling down an incline, in meters, and the base of the trapezoid represents the time interval between these positions in seconds, then

• What quantity is represented by the rise of the graph trapezoid and what are its units?  &&&&
• What quantity is represented by the run of the graph trapezoid and what are its units?  &&&&
• What quantity is represented by the slope of the trapezoid and what are its units?  &&&&
• What quantity is represented by the area of the trapezoid and what are its units?  &&&&
• What, if anything, does the slope represent?  &&&&
• What quantity is represented by the altitude of the equal-area rectangle and what are its units?  &&&&
• What quantity is represented by the base of the equal-area rectangle and what are its units?  &&&&
• What quantity is represented by does the area, if anything?  &&&&

Each answer should include a complete explanation, reasoned out from the geometry of the trapezoid and the definitions you gave at the beginning.

8.  If the altitudes of a ‘graph trapezoid’ represent the initial and final velocities of a ball rolling down an incline, in meters / second, and the base of the trapezoid represents the time interval between these velocities in seconds, then

• What is the slope of the trapezoid and what are its units?  &&&&
• What is the area of the trapezoid and what are its units?  &&&&
• What, if anything, does the slope represent?  &&&&
• What, if anything, does the area represent?  &&&& 

Each answer should include a complete explanation, reasoned out from the geometry of the trapezoid and the definitions you gave at the beginning.

9.  A ball rolls along a path, moving from position 20 cm to position 50 cm as its velocity increases from 5 cm/s to 15 cm/s.

• If its acceleration is uniform, then how long does this take, and what is the ball’s acceleration?    &&&&