# A2L Item 260

Goal: Interrelate representations of kinematical quantities

Source: CT151.2-10 An object’s motion is described by the graph above. The displacement
of the object during the entire 16 seconds is most nearly…

1. 200 meters
2. 250 meters
3. 300 meters
4. 350 meters
5. 400 meters
6. 450 meters
7. Cannot be determined

### Commentary:

(7) Students have difficulty reading graphs and finding areas.

# A2L Item 259

Goal: Interrelate representations of kinematical quantities

Source: CT151.2-8 An object’s motion is described by the graph above. The position of the
object at t = 9 seconds is most nearly…

1. 0 meters
2. 200 meters
3. 300 meters
4. 400 meters
5. 500 meters
6. Cannot be determined

### Commentary:

(6) This problem is primarily to determine if students appreciate the
information available from a graph. Many students will determine the
displacement forgetting that the initial position is unknown.

# A2L Item 197

Goal: Reasoning with magnetic forces

Source: UMPERG-283-626

In the following situations a charge q moves in a uniform magnetic
field. The strength of the magnetic field is indicated by the density
of field lines. In all cases the speed of the charge is the same. For
which situation(s) will the charge q have the largest displacement in a
given time T. 1. 1
2. 2
3. 3
4. 4
5. 5
6. 1 & 3
7. 2 & 4
8. 1, 2, 3 & 4
9. 1, 2, 3, 4 & 5
10. Cannot be determined

### Commentary:

(5) Since the speed cannot change, the greatest displacement will occur
when the path is a straight line. Some students may answer #10 thinking
that the time matters.

# A2L Item 196

Goal: Reasoning with magnetic forces

Source: UMPERG-283-625

In the following situations a charge q moves in a uniform magnetic
field. The strength of the magnetic field is indicated by the density
of field lines. In all cases the speed of the charge is the same. For
which situation(s) will the charge q travel the greatest distance in a
given time T? 1. 1
2. 2
3. 3
4. 4
5. 5
6. 1 & 3
7. 2 & 4
8. 1, 2, 3 & 4
9. 1, 2, 3, 4 & 5
10. Cannot be determined

### Commentary:

(9) The magnetic force can change the direction of the velocity but not
the speed. The distance traveled, therefore, cannot depend upon either
the strength or orientation of the magnetic field. It is important to
have students who pick one of the other choices verbalize their reasons.
Some students may interpret the question as asking for the
‘displacement’ and, thinking that the time is needed, respond #10.
Actually the result for displacement is #5.

# A2L Item 166

Goal: Problem solving and developing strategic knowledge

Source: UMPERG-ctqpe104

You are given this problem: A
block sits on a frictionless incline. Given the mass of the block, the
angle of incline, the distances d1 and d2, and
that the block starts from rest, find the time to travel from
d1 to d2.

What principle would you use to solve the problem MOST EFFICIENTLY?

1. Kinematics only
2. F = ma or Newton’s laws
3. Work-Energy theorem
4. Impulse-Momentum theorem
5. Angular Impulse-Angular Momentum
6. 1 & 2
7. 1 & 3
8. 2 & 3
9. None of the above
10. Not enough information given

### Commentary:

(6) Students responding #1 are relying on memory and would have
difficulty if a force other than gravity was involved.

# A2L Item 158

Goal: Hone the concept of displacement

Source: CT151.2-2

Bekki walks 3 m to the right, 4 m to the left, 5 m to the right, and 2 m
to the left. What is her displacement?

1. 0 m
2. 2 m
3. 2 m (to the right)
4. 2 m (to the left)
5. 14 m (to the right)
6. 8 m to the right and 6 m to the left
7. impossible to determine
8. none of the above

### Commentary:

(3) Students need to distinguish between distance and
displacement. Questions such as this are good introductions to vectors.

# A2L Item 154

Goal: Distinguish distance traveled from displacement

Source: CT151.2-1

Andy has the following series of displacements: 3 m to the right; 4 m to
the left; 5 m to the right; and 2 m to the left. What is his distance
traveled?

1. 0
2. 2 m
3. 2 m (to the right)
4. 2 m (to the left)
5. 14 m (to the right)
6. 8 m (to the right)
7. Impossible to determine
8. None of the above

### Commentary:

(8) Students just learning about vectors and displacements are
inclined to over specify quantities. Before they knew anything about
vectors they used distance as a scalar but can become confused and give
it the direction of the total displacement.

# A2L Item 141

Goal: Reasoning with kinetic energy and work

Source: UMPERG-ctqpe58 Two
blocks, M2 > M1, having the same kinetic energy
move from a frictionless surface onto a surface having friction
coefficient μk.

Which goes further before stopping?

1. M1
2. M1
3. Both go the same distance
4. Cannot be determined