Lillian C. McDermott

38

History

3/15/10

from kinematics and the other from dynamics – demonstrated the inability of many

students to relate basic concepts in mechanics to motions that they observe.

A.

Kinematics:

Confusion of Position, Velocity, and Acceleration

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David Trowbridge asked students to observe and compare the motions of two

identical steel balls as they rolled on adjacent tracks.

A strobe photograph shows the

positions of the balls at instants separated by equal time intervals.

(See the diagram.)

(a)

(b)

(c)

(d)

Speed Comparison Tasks 1 and 2.

In Speed Comparison Task 1, Ball A travels with uniform motion from left to right

while Ball B travels in the same direction, starting from rest at a point ahead of Ball A.

Ball A first passes Ball B but is later passed by Ball B.

The students are asked if the two

balls ever have the same speed.

(The students are not shown the strobe photos or graphs.)

In Speed Comparison Task 2, Ball A starts with a larger initial speed and moves up

the incline.

It never overtakes Ball B, which accelerates down the incline.

When asked

85

See Refs. 18 and 23.

Lillian C. McDermott

39

History

3/15/10

the same question as in Task 1, many students used a position criterion.

They claimed that

since the balls never passed each other, they never had the same speed.

A correct response in both tasks requires focusing attention on the separation

between the balls and identifying an instant when it appears to remain the same.

Our

standard for understanding was the ability to apply this criterion successfully to the

interpretation of simple motions.

Students often identified the instants when the balls

were at the same position as the instant when their velocities were the same.

The

following dialogue took place during an interview with a student who had completed the

algebra-based course.

(“I” represents the Investigator and “S” the represents the Student.)

I:

Now do either of these (instants of passing) represent instants when the balls

have the same velocity?

S: It would only be an instant.

If it was more than just an instant, maybe they

would go along the track side by side for a certain distance, but it’s actually

only about an instant that it has it.

Even analogies with everyday experience may not be enough to overcome the

confusion between speed and position.

For example, some students identified the moment

when one car passes another as the time when both cars have the same speed.

Acceleration Comparison Task 1

In Acceleration Comparison Task 1, students observe the motion of two steel balls

that roll down straight aluminum U channels that are side by side and inclined at the same