**Goal:** Differentiate between instantaneous and average acceleration.

**Source:** UMPERG

Below is shown a strobe diagram indicating the position of four objects

at successive time intervals. The objects move from left to right.

During the intervals shown, which object would you estimate has the

largest average acceleration?

- Object A
- Object B
- Object C
- Object D
- Objects A, B, & D
- Cannot estimate for (A) because its acceleration is changing
- Cannot estimate average acceleration from a strobe diagram
- None of the above
- Cannot be determined

## Commentary:

## Answer

(3) Assuming that the question is referring to magnitude, the largest

average acceleration is experienced by object (C). The other three

objects appear to start and end with approximately the same velocity.

For object (C) the velocity decreases in magnitude as the object moves

to the right. Students who answer (5) because they realize that the

average acceleration of C is negative and think zero is larger should

not be considered wrong.

## Background

It is important for students to develop multiple ways of interpreting

concepts. This ensures that students are not just following rote

procedures to answer questions. Once an idea is understood students

should be able to use their understanding in a variety of contexts and

with a variety of representations.

The concept of average acceleration depends only on the initial and

final velocity over some specified time interval. Some students will

make their judgments on the basis of changes in the velocity at

different points in the motion.

## Questions to Reveal Student Reasoning

How is the average acceleration determined? What is the difference

between average acceleration and instantaneous acceleration? Where is

the instantaneous acceleration greatest?

## Suggestions

Draw velocity vs. time graphs for the objects (A) and (B). Analyze the

average acceleration (instantaneous acceleration) for different time

intervals (times).