# A2L Item 016

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?

1. Object A
2. Object B
3. Object C
4. Object D
5. Objects A, B, & D
6. Cannot estimate for (A) because its acceleration is changing
7. Cannot estimate average acceleration from a strobe diagram
8. None of the above
9. Cannot be determined

### Commentary:

(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).