# A2L Item 004

Goal: Differentiate velocity and acceleration in the context of free-fall motion.

Source:

A person throws a ball straight up in the air. The ball rises to a maximum height and then falls back down so that the person catches it. Consider the ball while it is in the air.

Which of the following statements are true?

A. Just after the ball leaves the person’s hand the direction of the acceleration is up.

B. The acceleration is zero when the ball reaches its maximum height.

C. The acceleration is about 9.8 m/s2 (down) when the ball is falling.

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 are true
8. None are true
9. Cannot be determined

### Commentary:

After the ball leaves the person’s hand, its acceleration is 9.8 m/s2 (down) throughout the entire motion (assuming air resistance can be neglected). Answer (3) is the best choice.

#### Background

Use this item during kinematics, shortly after the introduction of “acceleration.” We suggest that students have some experience analyzing the velocity of objects undergoing freefall motion. Intended focus: (1) Do students think that the acceleration is zero at the maximum height, where the ball momentarily stops? (2) Do students think that the acceleration points in the same direction as the velocity? (3) Can students apply the definition of acceleration to a familiar situation?

The goal is to have students confront existing misconceptions:1) Students often believe that the acceleration must point in the direction of the motion; and 2) Students often believe that the acceleration is 9.8 throughtout free fall but zero at the top of the trajectory since the vertical speed is zero there.

#### Questions to Reveal Student Thinking

• What is the acceleration of the ball on the way up? What is the direction of the acceleration? Is the acceleration changing?
• What is the acceleration of the ball on the way down? What is the direction of the acceleration? Is the acceleration changing?
• How can you determine whether the acceleration is zero at the maximum height? Is the velocity of the ball changing at the maximum height?

#### Suggestions

Have students sketch the velocity of the ball as a function of time. Ask how the acceleration is related to this graph.

Using Microcomputer Based Lab software and a sonic ranger, generate a velocity graph for a cart going up and down an incline. Discuss how the graph relates to a velocity vs. time graph for a ball thrown vertically.