**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.