**Goal:** *Unspecified.*

**Source:** *Unspecified.*

An object’s motion is described by the graph:

What is the instantaneous velocity at t = 3s?

- 0 m/s
- 2 m/s
- 3 m/s
- 4 m/s
- 5 m/s
- Other

**Goal:** *Unspecified.*

**Source:** *Unspecified.*

An object’s motion is described by the graph:

What is the instantaneous velocity at t = 3s?

- 0 m/s
- 2 m/s
- 3 m/s
- 4 m/s
- 5 m/s
- Other

**Goal:** *Unspecified.*

**Source:** *Unspecified.*

An object’s motion is described by the graph:

What is the instantaneous velocity at t = 10s?

- 0 m/s
- 2 m/s
- 3 m/s
- 4 m/s
- 5 m/s
- Other

*None provided.*

**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…

- 200 meters
- 250 meters
- 300 meters
- 350 meters
- 400 meters
- 450 meters
- Cannot be determined

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

**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…

- 0 meters
- 200 meters
- 300 meters
- 400 meters
- 500 meters
- Cannot be determined

(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.

**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
- 2
- 3
- 4
- 5
- 1 & 3
- 2 & 4
- 1, 2, 3 & 4
- 1, 2, 3, 4 & 5
- Cannot be determined

(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.

**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
- 2
- 3
- 4
- 5
- 1 & 3
- 2 & 4
- 1, 2, 3 & 4
- 1, 2, 3, 4 & 5
- Cannot be determined

(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.

**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 d_{1}and d_{2}, and

that the block starts from rest, find the time to travel from

d_{1}to d_{2}.

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

- Kinematics only
- F = ma or Newton’s laws
- Work-Energy theorem
- Impulse-Momentum theorem
- Angular Impulse-Angular Momentum
- 1 & 2
- 1 & 3
- 2 & 3
- None of the above
- Not enough information given

(6) Students responding #1 are relying on memory and would have

difficulty if a force other than gravity was involved.

**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?

- 0 m
- 2 m
- 2 m (to the right)
- 2 m (to the left)
- 14 m (to the right)
- 8 m to the right and 6 m to the left
- impossible to determine
- none of the above

(3) Students need to distinguish between distance and

displacement. Questions such as this are good introductions to vectors.

**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?

- 0
- 2 m
- 2 m (to the right)
- 2 m (to the left)
- 14 m (to the right)
- 8 m (to the right)
- Impossible to determine
- None of the above

(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.

**Goal:** Reasoning with kinetic energy and work

**Source:** UMPERG-ctqpe58

Two

blocks, M_{2} > M_{1}, having the same kinetic energy

move from a frictionless surface onto a surface having friction

coefficient μ_{k}.

Which goes further before stopping?

- M
_{1} - M
_{1} - Both go the same distance
- Cannot be determined

(1) For a given amount of kinetic energy M1 will have a larger

velocity. The penetration distance depends upon the square of the

velocity.

Many students will notice that the relationship equating the kinetic

energy to work by friction has mass as a factor on both sides and will

answer #3. They are assuming that the masses have the same velocity, not

the same kinetic energy.

## Commentary:

None provided.