A2L Item 015
- Description: Compare the accelerations of two different objects. Underscores importance of both magnitude and direction.
- Goal: Differentiate between magnitude and direction of acceleration.
- Source: UMPERG
- Keywords: Acceleration, Mechanics
The question for students:
| 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 for teachers:
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.