# A2L Item 006

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.

1. Only (A)
2. Only (B)
3. Only (C)
4. Both (A) and (B)
5. Both (A) and (C)
6. Both (B) and (C)
7. All three motions have zero average acceleration
8. None has zero average acceleration
9. Can’t be determined

### Commentary:

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.