**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:** *Unspecified.*

**Source:** *Unspecified.*

An object’s motion is described by the graph:

What is the average velocity during the first 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:** Hone the concept of average velocity

**Source:** CTtil2;12;02

While traveling from Boston to Hartford, Person A drives at a constant

speed of 55 mph for the entire trip. Person B drives at 65 mph for half

the trip and then drives 45 mph for the second half of the trip. When

would B arrive in Hartford relative to A?

- B arrives before A.
- B arrives at the same time as A.
- B arrives after A.
- Not enough information.

(3) Many students are inclined to average the speeds and conclude that

they arrive at the same time. It is often useful to compare this

situation to the one in which time is halved.

**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:** Link acceleration to the slope of a velocity/time graph

**Source:** CT151.2-6

An

object’s motion is described by the graph above. The instantaneous

acceleration at t=10 sec is most nearly…

- 0 m/s
^{2} - -2 m/s
^{2} - 3 m/s
^{2} - -4 m/s
^{2} - 5 m/s
^{2} - Other

(1) Useful follow-up questions include; when does the object have

positive acceleration, when negative acceleration; does the object ever

stop?; when is it farthest from the origin?

**Goal:** Problem solving

**Source:** UMPERG-ctqpe118

A mass

m slides down a frictionless track of radius R=0.5m. As the mass

reaches the bottom, relative to the center of curvature, its angular

velocity is most nearly:

- 6 rad/sec
- 8 rad/sec
- 12 rad/sec
- 15 rad/sec
- 20 rad/sec
- Cannot be determined

(1) The velocity near the bottom can be found using energy

conservation.

**Goal:** Problem solving and developing strategic knowledge

**Source:** UMPERG-ctqpe103

You are given this problem:

A

block sits on a frictionless incline. Given the angle of incline, the

distance along the incline, and that the block is initially at rest,

find the speed after traveling a distance d.

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 and 2
- 1 and 3
- 2 and 3
- None of the above
- Not enough information given

(3) The change in gravitational potential can be found directly.

Alternately, the work done by the gravitational force must be equal to

the change in kinetic energy.

**Goal:** Problem solving with kinematics

**Source:** CT151.2-4

Ann is running with a constant speed of 3 m/s on a straight track. Deb

is also running with constant speed but is initially 10 m behind Ann. If

Deb catches up to Ann after Deb has traveled 55 m, how fast is Deb

running?

- 3.2 m/s
- 3.55 m/s
- 3.75 m/s
- 4.15 m/s
- More than 4.2 m/s
- none of the above
- cannot be determined

(6) The correct speed is 3.67 m/s. Students indicating #2 or #3

are likely making an arithmetic error. Have students graph the position

vs. time graphs for each runner.

## Commentary:

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