Category Archives: Middle School

Items appropriate for use in a middle-school physics or physical science course.

A2L Item 003

Goal: Hone the concept of acceleration.

Source: UMPERG

HOW MANY of the identified objects are NOT accelerating?

  • A race car going around a circular track at 150 MPH
  • A sky diver falling at a constant speed
  • A heavy box sliding across the floor, after being released
  • A bowling ball colliding with a pin
  • A vibrating guitar string
  • A baseball flying through the air
  • A child swinging on a swing

Enter the number of objects, or 8 for “none” and 9 for “cannot be determined”.

  1. One
  2. Two
  3. Three
  4. Four
  5. Five
  6. Six
  7. Seven
  8. None
  9. Cannot be determined

Commentary:

Answer

Only the skydiver, who has reached terminal velocity, has zero acceleration. In each of the other situations, the acceleration is nonzero because either the speed or the direction of motion is changing. Answer (2) is the best choice.

Background

Context for Use: Give after introducing the concept of acceleration. Intended focus: What factors/criteria do students use to determine whether an object is accelerating? The goal is to focus students on changes in the speed/direction of an object’s motion.

Questions to Reveal Student Reasoning

  • How do you know whether an object is accelerating? What are some examples of objects undergoing acceleration? If an object is falling is it necessarily accelerating?

  • In some cases did you need to make assumptions before deciding whether the object was accelerating? (Ask students to provide examples.)

Suggestions

Have students write out how they determine whether an object is accelerating. After discussing the different methods, have students vote on which one they think is best.

Play a “challenge game” with the class. Two teams of students think of situations in which an object undergoes some motion. The teams then take turns challenging each other to determine whether or not the objects are accelerating.

A2L Item 001

Goal: Relating physical understanding of an object’s motion to a graphical representation of acceleration.

Source: UMPERG

A soccer ball rolls slowly across the road and down a hill as shown below:

Which of the following sketches of ax vs. t is a reasonable representation of the horizontal acceleration of the ball as a function of time?

Commentary:

Answer

We will assume that rolling friction between the ball and road surface is small and that air resistance can be ignored. We will also assume that the ball does not leave the road surface at the top of the hill. If these assumptions are satisfied, the ball will roll across the level road at a (nearly) constant velocity. As it rolls down the hill, the ball will speed up, producing a constant acceleration in the direction of motion. There will be a nonzero component of acceleration pointing to the right. The graph at the right is a reasonable representation of the horizontal acceleration as a function of time. For our assumptions, answer (5) is the best choice.

Background

Context for Use: Give after students explore the vector nature of acceleration. Formal (quantitative) kinematics is not required.

Assessment Issues: (1) Can students recognize when an object is accelerating? What criteria do they use? (2) Do students perceive nonzero horizontal and vertical components of acceleration? Do some students think that the acceleration is in the y-direction only? (3) Do students think that the acceleration graph looks like the sketch of the road on which the ball rolls? What process do they use to construct a graph of acceleration versus time? (4) Do students confuse the different motion quantities? For example, do they interpret the graphs of acceleration versus time as velocity versus time graphs?

Questions to Reveal Student Reasoning

  • Where does the ball speed up? Where does it slow down? Why does its speed change?

  • What is the direction of the ball’s acceleration while it is on the hill? Does the ball accelerate to the right? Does the ball accelerate vertically?

Suggestions

Help students construct the horizontal (and vertical) velocity vs. time graph for the ball. If students have been exposed to forces, draw a free-body diagram and use it to find the net force.