Goal: Differentiate between magnitude and direction of acceleration.
Source: UMPERG
| Case | Column 1 | Column 2 |
| (A) | A car goes from 0 to 60 mph in 6s along a straight highway. |
A car goes from 60 to 0 mph in 6s along a straight highway. |
| (B) | A race car travels around a circular track at 50 mph. |
A race car travels around the same circular track at 100 mph. |
| (C) | A ball is thrown straight up. It rises 20 ft. Ignore the effects of the air. |
A ball is dropped straight down. It falls 20 ft. Ignore the effects of the air. |
For which cases is the acceleration the same for the motion described
in both columns?
- Case A only
- Case B only
- Case C only
- Cases A & B
- Cases B & C
- Cases A & C
- Cases A, B & C
- None of the cases
- Cannot be determined
Commentary:
Answer
(3) The only case having the same acceleration is C where the
acceleration is that due to the gravitational force. In case A, the
magnitude of the two accelerations is the same but one is positive and
the other negative, i.e. the vectors point in opposite directions.
[This assumes that the acceleration is uniform.] In case B, the
“direction” is the same, i.e. pointing toward the center of the circle,
but the magnitudes are different.
Background
This question reveals whether students have the concept of acceleration
as a vector (i.e. has direction as well as magnitude). Some students
may ignore the magnitude completely and key on the direction. The
objective here is to have students indicate the concept of acceleration
that they are using to answer the question.
Questions to Reveal Student Reasoning
For which cases is the magnitude of the acceleration the same? the
direction?
For which cases does the acceleration change during the motion
described?
Suggestions
Have students draw a motion diagram (a strobe diagram with the velocity
vector indicated at each position). This diagram helps students to
associate the acceleration with a change in velocity.