Summer Research Program for Science Teachers


Thomas Byrne

New Rochelle High School, Westchester

August 2003







How does the displacement, velocity and acceleration of a moving object change over time?







Objectives:  The student will be able to:

1)      Prepare graphs of the displacement vs. time, velocity vs. time and acceleration vs. time for a uniformly accelerated object.

2)      Describe the motion of an object through interpretation of such graphs.

3)      Work cooperatively to reach a consensus on problem presented and to explain solution of problem to class.



1)      Individual conceptual understanding sheets

2)      Group conceptual understanding sheets



1)      Students need to be familiar with the following terms:

a)      Scalar - A physical quantity, such as length and mass, characterized by magnitude only

b)      Vector - A quantity, such as velocity and force, described by both magnitude and direction; often depicted graphically by a directed line segment

c)      Distance - The total length of a path; a scalar quantity

d)      Displacement - The change of position of an object described by the vector that begins at the initial position of the object and ends at its final position

e)      Speed - The time rate at which a body travels distance; a scalar quantity

f)        Velocity - The time rate of change of displacement; a vector whose magnitude is speed and whose direction is the direction of motion

g)      Acceleration - The time rate of change of velocity; a vector quantity


Physical Science

CONTENT STANDARD B: As a result of their activities in grades 9-12, all students should develop an understanding of Motions and Forces 


2)      Discuss key concepts in graphing motion of uniformly accelerated object:

a)      distance and speed can never be negative

b)      the negative sign is an indication of direction for a vector

c)      the slope of the distance/time graph represents speed

d)      the slope of the displacement/time graph represents velocity

e)      the slope of the velocity/time graph represents acceleration

f)        the area under the velocity/time graph equals displacement



Unifying Concepts and Processes

STANDARD: As a result of activities in K-12, all students should develop understanding and abilities with the following concepts and processes:


3)      Hand out the first individual conceptual understanding sheet (PDF file), “Driving to Nicole’s House," and instruct students to work on the problem individually.


4)      After students have had a sufficient time to think about the problem and record their responses, arrange class in groups of three (mixed-level students) and give each group a group conceptual understanding sheet  (PDF file).  Students are instructed to discuss each other's ideas. The purpose of the discussion is to allow them to clarify what they think, discover faults in their reasoning and finally reach consensus on the answer to the problem.  They then record their answer on the group conceptual understanding sheet.  All group responses are placed on the board.  During the discussions, the teacher should move around the room, clarifying points about the exercise if needed but avoiding getting involved in the discussions.



Teachers of science guide and facilitate learning. In doing this, teachers


5)      Each group records its answer on the group conceptual understanding sheet and all such sheets are displayed at the front of the room. Each member of the group out to be prepared to defend their group's answer to the whole class.


6)      Homework/Extension:  Students can practice the skills of graphing uniformly accelerated motion learned in class through use of the many Java applets available online.  See, for example, for a list of links.



Teachers of science design and manage learning environments that provide students with the time, space, and resources needed for learning science. In doing this, teachers


Teachers of science develop communities of science learners that reflect the intellectual rigor of scientific inquiry and the attitudes and social values conducive to science learning. In doing this, teachers


7) A similar exercise can be conducted regarding the acceleration and velocity of an object in free-fall.

8)      This approach to conceptual understanding in physics is based upon the CUP method developed at Monash University, Australia:



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