Gregg Wolfe; Erika Gasper; John Stoke; Julie Kretchman; David Anderson; Nathan Czuba; Sudhi Oberoi; Liza Pujji; Irina Lyublinskaya; Douglas Ingram

2.1 Displacement

1.

Which of the following statements comparing position, distance traveled, and displacement is correct?

An object may record a distance traveled of zero while recording a non-zero displacement.
An object may record a non-zero distance traveled while recording a displacement of zero.
An object may record a non-zero distance traveled while maintaining a position of zero.
An object may record a non-zero displacement while maintaining a position of zero.

2.2 Vectors, Scalars, and Coordinate Systems

2.

A student is trying to determine the acceleration of a feather as she drops it to the ground. If the student is looking to achieve a positive velocity and positive acceleration, what is the most sensible way to set up her coordinate system?

Her hand should be a coordinate of zero and the upward direction should be considered positive.
Her hand should be a coordinate of zero and the downward direction should be considered positive.
The floor should be a coordinate of zero and the upward direction should be considered positive.
The floor should be a coordinate of zero and the downward direction should be considered positive.

2.3 Time, Velocity, and Speed

3.

A group of students has two carts, A and B, with wheels that turn with negligible friction. The two carts travel along a straight horizontal track and eventually collide. Before the collision, cart A travels to the right and cart B is initially at rest. After the collision, the carts stick together.

Describe an experimental procedure to determine the velocities of the carts before and after the collision, including all the additional equipment you would need. You may include a labeled diagram of your setup to help in your description. Indicate what measurements you would take and how you would take them. Include enough detail so that another student could carry out your procedure.
There will be sources of error in the measurements taken in the experiment both before and after the collision. Which velocity will be more greatly affected by this error: the velocity prior to the collision or the velocity after the collision? Or will both sets of data be affected equally? Justify your answer.

2.4 Acceleration

4.

The picture is a graph grid showing v (ms) along the vertical y-axis and t (s) near the center of the graph for the horizontal x-axis. The v(ms) axis is labeled from top to bottom, 10, 8, 6, 4, 2, 0 (t axis), -2, -4, -6. Each of the even numbers has a horizontal gray line running the width of the grid. The t axis is labeled with a vertical tic, a second vertical tic and 1.0 at the third vertical tic. There are two more vertical tics and then 2.0 at the sixth vertical tic. Each tic has a vertical gray line running the height of the grid. There are 5 black points labeled A-E on the grid with a solid black line connecting the points. The points on the graph are as follows along the t, V (or x-y grid): A is at the origin (0,0). B is at the second tic (2/3 second) and 8 v/s. The line between A and B rises quickly: It is past half-way between 6 and 8 in the first tic and is a very short curve between the first and second tic. C is at the third tic (1.0) and 8 v/s. The line between B and C is horizontal and goes from the second to third tics on the grid. D is on the horizontal axis in the middle of the grid (V of 0 m/s) at a point just slightly past the first tic after 1. The from C to D is straight. E is at -4 on the vertical axis and 2.0 on the horizontal axis. The line is straight between D and E and moves to gray boxes right and two gray boxes down.

Figure 2.84 Graph showing Velocity vs. Time of a cart.

A cart is constrained to move along a straight line. A varying net force along the direction of motion is exerted on the cart. The cart's velocity v as a function of time t is shown in the graph. The five labeled points divide the graph into four sections.

Which of the following correctly ranks the magnitude of the average acceleration of the cart during the four sections of the graph?

a_CD > a_AB > a_BC > a_DE
a_BC > a_AB > a_CD > a_DE
a_AB > a_BC > a_DE > a_CD
a_CD > a_AB > a_DE > a_BC

5.

Push a book across a table and observe it slow to a stop.

Draw graphs showing the book's position vs. time and velocity vs. time if the direction of its motion is considered positive.

Draw graphs showing the book's position vs. time and velocity vs. time if the direction of its motion is considered negative.

2.5 Motion Equations for Constant Acceleration in One Dimension

6.

A group of students is attempting to determine the average acceleration of a marble released from the top of a long ramp. Below is a set of data representing the marble's position with respect to time.

Position (cm)	Time (s)
0.0	0.0
0.3	0.5
1.25	1.0
2.8	1.5
5.0	2.0
7.75	2.5
11.3	3.0

Table 2.2

Use the data table above to construct a graph determining the acceleration of the marble. Select a set of data points from the table and plot those points on the graph. Fill in the blank column in the table for any quantities you graph other than the given data. Label the axes and indicate the scale for each. Draw a best-fit line or curve through your data points.

Using the best-fit line, determine the value of the marble's acceleration.

2.7 Falling Objects

7.

Observing a spacecraft land on a distant asteroid, scientists notice that the craft is falling at a rate of 5 m/s. When it is 100 m closer to the surface of the asteroid, the craft reports a velocity of 8 m/s. According to their data, what is the approximate gravitational acceleration on this asteroid?

0 m/s²
0.03 m/s²
0.20 m/s²
0.65 m/s²
33 m/s²

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