**Goal:** Contrast instantaneous and average acceleration. Explore the difference between them.

**Source:** UMPERG

Which of the following motions has a zero value for the average

acceleration during the specified time interval?

A. A race car makes one lap around an oval track at constant speed.

The time interval is the time to complete the lap.B. A cart collides with a wall and rebounds with the same speed. The

time interval is the time during which the cart is in contact with the

wall.C. A ball rolls up, then down a hill. The time interval is the time

the ball is on the hill.

- Only (A)
- Only (B)
- Only (C)
- Both (A) and (B)
- Both (A) and (C)
- Both (B) and (C)
- All three motions have zero average acceleration
- None has zero average acceleration
- Can’t be determined

## Commentary:

## Answer

Situation A is the only one where the velocity is the

same at the beginning and end of the time interval. Therefore, it is

the only situation where the change in velocity is zero. Answer (1) is

the best choice.

## Background

Use this item early in the

study of acceleration. It requires that students be familiar with the

definition of average acceleration. Issues: (1) Do students have a

working knowledge of the vector nature of velocity and acceleration?

(2) Do students incorrectly think that the average acceleration must be

zero if an object’s speed is the same at the beginning and end of the

time interval, even if the direction of the velocity vector at these two

times is different. (3) Do students correctly perceive that the

velocity is different when an object changes direction?

## Questions to Reveal Student Reasoning

What is the definition of average

acceleration? How do you compute the average acceleration for a given

time interval?

How can you tell if the velocity has changed? If an object has the same

speed at two different times, is the average acceleration necessarily

zero? Why, or why not?

What are some good rules of thumb for ascertaining whether or not the

average acceleration of an object is zero for a given time interval?

## Suggestions

Have students write out examples of motion

for a finite time interval. Have students present their examples to the

class. Have the class decide whether the average acceleration is zero.

Let the class devise ways of determining whether the average

acceleration in a certain situation is zero.