**Goal:** Honing the idea of constant acceleartion.

**Source:** UMPERG

A baseball is shot into the air from a spring loaded cannon. The diagram shows the ball at five locations. At which location is the magnitude of the acceleration least?

- Position A
- Position B
- Position C
- Position D
- Position E
- Position B and D
- Position A and E
- None of the Above
- Cannot be Determined

## Commentary:

## Answer

The ball’s acceleration is 9.8 m/s

^{2}(down) throughout itsentire motion (assuming air resistance can be neglected). Answer (8) is

the best choice.

## Background

Students should have some experience analyzing the velocity of objects

undergoing free-fall motion. Issues to consider: (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 throughout free fall but zero at the top of the trajectory since the

vertical speed is zero there.

## Questions to Reveal Student Reasoning

direction of the acceleration? Is the acceleration changing?

direction of the acceleration? Is the acceleration changing?

height? Is the velocity of the ball changing at the maximum height?

## Suggestions

Ask students to apply the operational definition of acceleration (take

the velocity vector just after C and subtract the velocity vector just

before C and divide by the time interval). Have them compare the x/y

component of the velocity just before C with the x/y component of the

velocity just after point C.

For students who persist in thinking that both the velocity and

acceleration are zero at the top of a trajectory, contrast the

subsequent motion with that of an object sitting at rest on a surface.