A Conceptual Approach To Teaching KinematicsMark Rosenquist and Lillian

McDermott

A Review byMarsha Turin and Lisa

HendersonTechBoston Academy

Topics in KinematicsInstantaneous velocity as a limitDistinguishing between position and velocityDistinguishing velocity, change of velocity and accelerationMaking connections among graphs, concepts and motions

Instantaneous Velocity As A Limit

The concept was developed via lab experimentation and pencil and paper exercises involving nonuniform motion.The concept was defined based on the students lab and pencil and paper observations in order to make the concept concrete.The concept was defined as the time interval that motion appeared uniform.

Summary of MethodsLab Exercise

Examination of ticker tape motion diagrams generated by an accelerating fan cart and a ticker tape timer. Examine the dots for uniform motion.

Pencil and Paper Exercise Students plotted a magnified section of a curved position vs. time graph until the motion appears uniform.

Distinguishing Between Position and Velocity

MisunderstandingStudents incorrectly interpret position vs. time graphs.

Samespeed

Same speed

x

t

Addressing The Misunderstanding

Used lab demonstrations to concretely distinguishing position and velocity over time.Part I

2 balls, 2 tracks, one ball moves uniformly, the other accelerates2 balls, 2 tracks, balls move uniformly, one ball starts ahead of the other2 balls, 2 tracks,balls move with different uniform velocities, one ball passes the other.

Addressing The Misunderstanding

Part II2 balls, 2 tracks, one ball has positive acceleration, the other has a negative acceleration, no passing takes place.

v

t

x

t

Distinguishing Velocity, Change of Velocity and

AccelerationClarification of these concepts as distinctHelps students associate a particular velocity with a particular timeHelps students recognize the necessity of considering the time interval during which a change in velocity occursRequires students to apply the definition of acceleration in comparing two real motions

Instantaneous Velocity Experiment

Students are asked to compare the motion of a ball rolling down a track with that of a marked revolving belt of constant velocity

2-3 meters

Belt marked in 10 cm segments

Comparing Belt and Ball Speed

Students determine belt speed by timing movement of a given mark over a given distanceAs the ball rolls down the incline its velocity, relative to the constant velocity belt changes

Students Gain Immediacy of Trial and Results

This differs from traditional methods as the velocity is measured directly rather than as a derivation of position graphsVelocity at any moment is therefore determined during the experiment rather than some time after

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Timing the ball’s ProgressStudents start a stopwatch when they release the ballWhen the ball’s velocity matches that of the belt the stopwatch is stoppedStudents measure the time it takes for the ball to attain this velocityStudents plot data for several speeds and trials

Combining Immediacy and Tactile Experience

Students see instantaneous velocity as they see the ball’s motion overtake that of the constant speed beltThe physical act of starting and stopping the stopwatch draws student’s attention to the changing time intervalsThey see the ball speed up and have to respond to how quickly the increase in speed occurs

Increased Complexity with 2 Moving Balls

This is followed by comparing the motion of two balls rolling down inclines of differing degreeStudents analyze the accelerations of the two balls by comparing their relative positions and motion

Comparing the Motion of Two Moving Balls

A

B

Greater initial velocity, then greater acceleration

Separation constant

Discussion and AnalysisCiting the moment that the ball’s motion is the same, students incorrectly assess that acceleration is the same.Instructor is then able to direct students to “instantaneous” velocitiesStudents are able to separate the concepts of velocity and acceleration through analysis of their own observations

GraphsStudents graph the motions they have seenCreate situations that will match graphsRecognize that different graphs can represent the same motion using different axes

ACTIVE PHYSICS LOOKS AT ACCELERATION

Students are asked to analyze the motion with respect to the spacing of the dotsStudents recognize that the spacing of the dots correlates to the motion that they observed in the moving cart * * * * * * * * * * * * * *

STUDENTS LOOK AT SEGMENTS OF THE

MOTIONStudents are asked to look at the segment where the motion is fastest and slowestThey correlate what they “know” with what they observe in the dotsThis brings them close to an understanding of instantaneous velocity

Carl Lewis and GraphsStudents are asked to determine how accurately they can assess Carl Lewis’s speed.Students recognize that they are given 10 meter increments and cannot immediately determine an “instantaneous” velocity, although this term is not introduced in the text, the opportunity for the teacher is there

Two Motions time per Interval

0

0.5

1

1.5

2

0-10 10.0-20

20-30

30-40

40-50

50-60

60-70

70-80

80-90

90-100

time per Interval

understanding sprints

0

24

6

8

1012

14

0-10 10.0-20

20-30

30-40

40-50

50-60

60-70

70-80

80-90

90-100

distance

sp

ee

d

Speed

As the time it takes to cover 10 m decreases…

Velocity increases