Physics midterm question: distance traveled vs. displacement

Physics 205A Midterm 1, fall semester 2019
Cuesta College, San Luis Obispo, CA

The v_x(t) graph of a Physics 205A student walking along a horizontal road is shown at right. The student started at x = 0 at t = 0. Discuss whether the magnitude of the distance traveled by the student is equal to or greater than the magnitude of the displacement. Explain your reasoning using the properties of velocity, position, time, distance traveled, and/or displacement.

Solution and grading rubric:

• p:
  Correct. Demonstrates that the distance traveled is equal to the magnitude of displacement, as the student always travels in the same (positive) direction (only positive horizontal velocity values), without reversing direction (no negative horizontal velocity values).
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Conceptual understanding of displacement and distance traveled, but somehow misinterprets/misapplies/ignores the given information.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01duCk
p: 38 students
r: 0 students
t: 5 students
v: 4 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 5808):

Physics midterm question: cargo-loaded truck vs. truck-loaded cargo

Physics 205A Midterm 1, fall semester 2019
Cuesta College, San Luis Obispo, CA

A Physics 205A student draws a (correct) free body diagram for a 600 kg cargo load resting on a stationary 11,000 kg truck with these two forces[*]:

Weight force of Earth on cargo load (5,800 N, downwards),

Normal force of truck on cargo load (5,800 N, upwards).

This student additionally claims that "this [free body diagram for the cargo load] would change if the truck was on top of the cargo load." Discuss why both the magnitude and direction of the normal force of truck on the cargo load would change if the truck were instead resting on top of the cargo load, and how you know this. Explain your reasoning using free-body diagram(s), the properties of forces, and Newton's laws.


[*] waiferx.blogspot.com/2017/10/physics-midterm-question-proposed-test.html.

Solution and grading rubric:

• p:
  Correct. Complete free-body diagram(s), and discusses/demonstrates that when the truck is on top of the cargo load:
  1. the truck has two vertical forces acting on it:

     Weight force w of Earth on truck (m_truck·g = 107,800 N, downwards),
     Normal force N of cargo load on truck (107,800 N, upwards),

     and since there is no vertical motion, these two vertical forces must be equal in magnitude due to Newton's first law; and
  
  
  2. from Newton's third law, these two forces must have equal magnitudes and opposite directions:

     Normal force Nof cargo load on truck (107,800 N, upwards),
     Normal force Nof truck on cargo load (107,800 N, downwards),

     such that the normal force of truck on cargo load for the case where the truck is on top of the cargo load is both different in magnitude (107,800 N vs. 5,800 N) and direction (downwards vs. upwards) compared to the normal force of truck on cargo load in the case where the cargo load was on top of the truck.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically application of Newton's third law is problematic, or only implied, but still discusses how the normal force of truck on the cargo load is both different in magnitude and direction than in the previous case.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some substantive attempt at analyzing forces using Newton's laws and free-body diagrams.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at using Newton's laws and free-body diagrams.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic attempt at using Newton's laws and free-body diagrams.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01duCk
p: 17 students
r: 16 students
t: 18 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1995):

Physics midterm question: pulled box pulling on table underneath

Physics 205A Midterm 1, fall semester 2019
Cuesta College, San Luis Obispo, CA

A Physics 205A student applies a force (magnitude of 32 N, directed to the left) to pull on a rope attached to a 12.0 kg box, which moves at constant speed to the left across a fixed, stationary table. Discuss why both the magnitude and direction of the kinetic friction force of the box on the table would also be 32 N, directed to the left. Explain your reasoning using free-body diagram(s), the properties of forces, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Complete free-body diagram(s), and discusses/demonstrates:
  1. the box has two horizontal forces acting on it:

     Tension force T of student on box (32 N, to the left),
     Kinetic friction force  f_k of table on box (32 N, to the right),

     and since the box has a constant velocity ("constant speed to the left"), these two horizontal forces must be equal in magnitude due to Newton's first law; and
  
  
  2. from Newton's third law, these two forces must have equal magnitudes and opposite directions:

     Kinetic friction force  f_k of table on box (32 N, to the right),
     Kinetic friction force  f_k of box on table (32 N, to the left).

• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some substantive attempt at analyzing forces using Newton's laws and free-body diagrams. Typically discusses Newton's first law for the forces acting on the box, but subsequent discussion of Newton's third law is omitted or merely implied.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at using Newton's laws and free-body diagrams.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic attempt at using Newton's laws and free-body diagrams.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01duCk
p: 15 students
r: 5 students
t: 14 students
v: 15 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 6900):
Another sample "p" response (from student 2533; note that the static friction force of the ground on table pointing to the right is denoted as a tension force):
A sample "t" response (from student 1995), discussing Newton's first law for the box, demonstrating that the kinetic friction force of the table on the box points to the right with a magnitude of 32 N:

Physics quiz question: comparing horizontal velocity components

Physics 205A Quiz 3, fall semester 2019
Cuesta College, San Luis Obispo, CA

Two velocity vectors shown at right have different speeds and directions. All angles are measured counterclockwise from the +x axis. Velocity vector __________ has the larger horizontal component magnitude.
(A) v_A.
(B) v_B.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

Since these θ angles are measured counterclockwise from the +x axis, the horizontal components of these velocity vectors are given by:

v_A,x = v_A·cosθ_A,
v_B,x = v_B·cosθ_B.

Then the horizontal components are these velocity vectors can be calculated and compared:

v_A,x = v_A·cosθ_A = (10 m/s)·cos(80°) = 1.736481776669303... m/s,

or to two significant figures, the horizontal component of v_A has a magnitude of 1.7 m/s, while:

v_B,x = v_B·cosθ_B = (4.0 m/s)·cos(60°) = 2.0 m/s.

Thus the horizontal component of v_B is greater than the horizontal component of the horizontal component of v_A.

Sections 70854, 70855
Exam code: quiz03Ch3V
(A) : 4 students
(B) : 49 students
(C) : 1 student
(D) : 0 students

Success level: 91%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.19

Physics quiz question: soccer ball vertical velocity component

Physics 205A Quiz 3, fall semester 2019
Cuesta College, San Luis Obispo, CA

A Physics 205A student kicks a soccer ball off a cliff with an initial velocity vector that has x- and y-components:

v_0x = +6.1 m/s,
v_0y = –3.2 m/s.

Neglect air resistance. Just before it hits the ground, the magnitude of the soccer ball's vertical velocity is:
(A) 0 m/s.
(B) some value between 0 m/s and 3.2 m/s.
(C) 3.2 m/s.
(D) some value greater than 3.2 m/s.

Correct answer (highlight to unhide): (D)

While the horizontal component of the soccer ball's velocity never changes, the vertical component of the soccer ball's velocity will always keep changing, due to the acceleration due to gravity. The soccer ball already starts with an initial downwards speed, and the vertical downwards speed will increase as it keeps moving along its trajectory.

Sections 70854, 70855
Exam code: quiz03Ch3V
(A) : 6 students
(B) : 5 students
(C) : 19 students
(D) : 24 students

Success level: 44%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.86

Physics quiz question: Kia Telluride braking time

Physics 205A Quiz 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

"2020 Kia Telluride"
Automotive Rhythms
flic.kr/p/2eei8ws

According to Car and Driver magazine[*] a 2020 Kia Telluride SX AWD sports utility vehicle was able to slow down from an initial speed of 31 m/s to a complete stop over a distance of 49 m. Assume that the road is horizontal, and that the acceleration of the Kia Telluride is constant and always points in the opposite direction from its velocity. While the Kia Telluride slowed down to a complete stop, the elapsed time was:
(A) 0.057 s.
(B) 0.32 s.
(C) 1.8 s.
(D) 3.2 s.

[*] David Beard, "The 2020 Kia Telluride Is Set to Win Big in the Three-Row SUV Segment," caranddriver.com/reviews/a26965174/2020-kia-telluride-drive/.

The following quantities are given (or assumed to be known):

(t₀ = 0 m),
(x₀ = 0 m),
x = +49 m,
v_0x = +31 m/s,
v_x = 0 m/s.

So in the equations for constant (average) acceleration motion in the horizontal direction, the following quantities are unknown, or are to be explicitly solved for:

v_x = v_0x + a_x·t,

x = (1/2)·(v_x + v_0x)·t,

x = v_0x·t + (1/2)·a_x·(t)²,

v_x² = v_0x² + 2·a_x·x.

With the unknown quantity t to be solved for appearing in the second equation, with all other quantities given (or assumed to be known), then:

x = (1/2)·(v_x + v_0x)·t,

t = 2·x/(v_x + v_0x) = 2·(+49 m)/(+31 m/s + 0 m/s) = 3.1612903226 s,

or to two significant figures, t = 3.2 s.

(Response (A) is sqrt(v_x)/(2·x); response (B) is v_x/(2·x); response (C) is sqrt(v_x/(9.80 m/s²)).)

Sections 70854, 70855
Exam code: quiz02Cs1o
(A) : 2 students
(B) : 4 students
(C) : 4 students
(D) : 44 students

Success level: 81%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46

Physics quiz question: comparing distances traveled

Physics 205A Quiz 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

The v_x(t) graph of a Physics 205A student moving along a straight line is shown at right, drawn with a solid line. The student started at x = 0 at t = 0. The student traveled a farther distance during the time interval:
(A) 0 s ≤ t ≤ 7 s.
(B) 7 s ≤ t ≤ 10 s.
(C) (There is a tie.)
(D) (Not enough information given.)

Correct answer (highlight to unhide): (C)

The displacement of the student is the area bounded by the student's v_x(t) graph and the time axis. Since the student is always traveling in the forward direction (as all the velocity values are positive during this time interval), then the distance traveled is the same as its displacement.

For 0 s ≤ t ≤ 7 s, the bounded area can be broken up into a triangle with an adjacent square:

∆x = (1/2)·(5 s)·(2 m/s) + (2 s)·(2 m/s),

∆x = 5 m + 4 m = 9 m.

For 7 s ≤ t ≤ 10 s, the bounded area can be broken up into a rectangle with a triangle atop it:

∆x = (2 s)·(3 m/s) + (1/2)·(3 s)·(2 m/s),

∆x = 6 m + 3 m = 9 m.

Thus the student travels the same distance (9 m) during the 0 s ≤ t ≤ 7 s and the 7 s ≤ t ≤ 10 s time intervals.
Sections 70854, 70855
Exam code: quiz02Cs1o
(A) : 24 students
(B) : 6 students
(C) : 22 students
(D) : 1 student

Success level: 41%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.88

Physics quiz question: Casio watch prototype testing

Physics 205A Quiz 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

Casio engineer Kikuo Ibe tested G-Shock watch prototypes by placing them in a rubber ball dropped from a window, falling 10 m down to the ground[*]. Neglect air resistance. Choose up to be the +y direction.

"Story"
Casio America Inc.
gshock.com/technology/story

After being released from rest, the rubber ball took __________ to reach the ground.
(A) 0.49 s.
(B) 1.0 s.
(C) 1.4 s.
(D) 2.0 s.

[*] gshock.com/technology/story.

Correct answer (highlight to unhide): (C)

The following quantities are given (or assumed to be known):

(t₀ = 0 s),
(y₀ = 0 m),
y = –10.0 m (below the starting point),
v_0y = 0 m/s (no initial velocity),
a_y = –9.80 m/s².

So in the equations for constant acceleration motion in the vertical direction, the following quantities are unknown, or are to be explicitly solved for:

v_y = v_0y + a_y·t,

y = (1/2)·(v_y + v_0y)·t,

y = v_0y·t + (1/2)·a_y·(t)²,

v_y² = v_0y² + 2·a_y·y.

With the unknown quantity t to be solved for appearing in the third equation, with all other quantities given (or assumed to be known), then:

y = v_0y·t + (1/2)·a_y·(t)²,

(–10.0 m) = (0 m/s)·t + (1/2)·(–9.80 m/s²)·t²,

1.4285714286 s = t,

or to two significant figures, the elapsed time for the rubber ball to fall is 1.4 s.

(Response (A) is a_y/(2⋅y); response (B) is sqrt(y/a_y); response (D) is 2·y/a_y.)

Sections 70854, 70855
Exam code: quiz02Cs1o
(A) : 2 students
(B) : 17 students
(C) : 29 students
(D) : 6 students

Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.72

Physics quiz archive: kinematics, free fall

Physics 205A Quiz 2, fall semester 2019
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855
Exam code: quiz02Cs1o



Sections 70854, 70855 results

0- 6 :
7-12 :	******** [low = 9]
13-18 :	************
19-24 :	****************** [mean = 21.1 +/- 6.0]
25-30 :	**************** [high = 30]

Online reading assignment: free fall, vector components

Physics 205A, fall semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on free fall and vector components.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"How to find the right variables for a problem by analyzing which parts of the information are given and which are not. I also understand how to determine which of the kinematic equations to use by determining which of the five variables needs to be found and how to rule out a variable that doesn't need to be found."

"Things can be thrown upwards (start with positive velocity), thrown downwards (start with negative velocity), or dropped (start with zero velocity)."

"During free fall, air resistance is neglected and the acceleration is nearly constant. Because acceleration is constant, we can use kinematic equations. Using a right triangle we are able to define sinθ cosθ and tanθ which helps us solve problems that involve angles. Scalars are numbers with magnitude such as time and volume while vectors are quantities with magnitude and direction such as displacement and velocity."

"I understand that an object can have a different vertical distance traveled than magnitude of vertical displacement. This is dependent on if the object is thrown straight in the air and then free falls, dropped into free fall, or thrown downward. I believe that the vertical displacement is equal to the distance if the object is dropped or thrown down, but the distance traveled is GREATER than the displacement if the object is thrown up."

"The fact that the only force acting on a ball falling down is gravity which has a constant acceleration is consistent with my understanding of physics. I also understand that vectors are determined by the x and y components in a triangle bringing us back to trigonometry.

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I was confused about how an object thrown or shot upwards can reach the same speed when it comes back down to its initial starting point as when it is thrown or shot downwards from its starting point."

"I found the homework problems a little bit confusing just because we haven't gone over many of those sorts of problems together. It would be very helpful to go over one of those specific problems in lecture."

"Trigonometry, but just a refresher would be useful.

Explain what assumptions are made about the amount of drag (air resistance) on an object said to be in free fall.

"We assume that drag forces are negligible."

"Air resistance is ignored."

A boy steps off of a ledge (with no initial vertical velocity) and splashes into the water below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	*********** [11]
zero.	********************************* [33]
positive.	*** [3]
(Unsure/guessing/lost/help!)	** [2]

For the boy, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	*** [3]
equal to.	************************************ [36]
greater than.	******** [8]
(Unsure/guessing/lost/help!)	** [2]

A ball is thrown and released downwards from the top of a building, and hits the ground below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	************************* [25]
zero.	********** [10]
positive.	********* [9]
(Unsure/guessing/lost/help!)	***** [5]

For the ball, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	***** [5]
equal to.	**************************** [28]
greater than.	****************** [13]
(Unsure/guessing/lost/help!)	*** [3]

A hat is thrown and released upwards into the air and lands on the grass below.

Choose up to be the +y direction. The initial vertical velocity v_0y has a __________ value.

negative.	**** [4]
zero.	****** [6]
positive.	*********************************** [35]
(Unsure/guessing/lost/help!)	**** [4]

For the hat, the vertical distance traveled is __________ the magnitude of the vertical displacement.

less than.	***** [5]
equal to.	*** [3]
greater than.	************************************** [38]
(Unsure/guessing/lost/help!)	*** [3]

Mark the level of your exposure to trigonometry (triangles, unit circles, inverse functions, Pythagorean theorem):

None at all.	* [1]
Slight.	*** [3]
Some.	********** [10]
A fair amount.	************************ [24]
A lot.	*********** [11]

Indicate the following trigonometric relations between angle θ, the opposite leg o, the adjacent leg a, and hypotenuse h for a right triangle. (Assume that the angle θ is in the first quadrant: 0° ≤ θ ≤ 90°.)
(Only correct responses shown.)

sin θ: (o/h) [92%]
cos θ: (a/h) [88%]
tan θ: (o/a) [88%]
hypotenuse h length: √(o² + a²) [94%]

Describe what mnemonic device (if any) you use to memorize the right-triangle trigonometric relationships.

"Soh-cah-toa."

"Don't recall one."

"I've never heard one."

"I don't really use one."

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"This is pretty cool. We are now moving into free fall which might start to make some things confusing and interesting when combining it with our horizontal motion knowledge."

"For the free fall examples above, would ground level be 0 or from when the ball left their hand?" (The convention used here is that we will always start at y = 0 at t = 0.)

"For all of the questions in this assignment, all of the initial velocities are zero? Because everything starts from not moving and is then thrown?" (If you throw a ball, it won't be in free fall (subject only to the force of gravity) until you let it go--so we can only start time t = 0 from the moment it was released with an initial velocity, as it leaves your hand.)

"Is there ever a setting where the free fall rules for falling objects don't apply?" (If air resistance (drag) is significant, then we can't say that acceleration is a constant value of 9.80 m/s² downwards.)

"In terms of this class are we to automatically assume drag/air resistance doesn't matter or will it be noted?" (On the quizzes and midterms, it will always be stated whether or not air resistance is negligible.)

"The last time I used SOH CAH TOA was 10th grade, so it's a little fuzzy."

"Will we only be using trigonometry to solve problems? I like calculus but I get lost when it comes to applying it to physics for some reason." (We'll use trigonometry to break down diagonal vectors such that we can analyze horizontal and vertical motion separately for projectile motion.)

"Nothing to ask here. Looking forward to the lecture!"

Online reading assignment: constant acceleration equations of motion

Physics 205A, fall semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and reviewing a flipped class presentation on (constant acceleration) motion.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I am starting to understand the 'chain of pain' much more now, especially after the practice we had in lecture last week."

"Position-time graphs and velocity-time graphs are becoming easier to read and understand with the help of the 'chain of pain.' The more I look at the chain of pain and the graphs, that more they appear logic-based."

"I have a much better understanding of chord and tangent slopes. A chord slope touches two different points on a graph, and therefore represents an average; whereas a tangent slope only touches one point on the graph, providing instantaneous information."

"I understand the how and why of the 'chain of pain,' though I have yet to memorize it."

"We can solve one-dimensional motion problems using kinematic equations by determining the known and unknown variables and then selecting the appropriate equation(s) to solve for the unknowns. These equations only apply when acceleration is constant."

"There are four equations we need to know regarding time, velocity, acceleration, and position. We need to know three variables per equation in order to solve for the fourth introduced variable or else it isn't solvable."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I am still confused about the 'chain of pain' chart. I am not sure what the arrows lead to and how to figure out how to solve a problem using it."

"After attending the class last Wednesday, the 'chain of pain' was not as confusing as it was earlier. The hardest part is just memorizing each process and how to get to each piece of the chart."

"The kinematic graphs are still confusing to me; I need to memorize the 'chain of pain' and how to find chord and tangent slope."

"The constant acceleration equations. I am unsure of when they are supposed to be used during certain equations."

"I am struggling with deciding which constant acceleration equation to use for these problems. It's difficult for me to confirm which quantities are given, especially with the UAV example."

"I am still a bit unsure of how to extract what the problem gives and then plug that information into the equations. I am also still a bit confused on picking the best kinematic equation. I know you pick based off of what information is given, but extracting the information proves to be a bit difficult for me."

"Not much at all. You just have to pay attention to what the problems are asking for."

Mark the level of your expertise in algebraically solving multiple equations for multiple unknowns.

None at all.	* [1]
Slight.	* [1]
Some.	************* [14]
A fair amount.	********************** [22]
A lot.	****** [6]

"2012 Chrysler 300 - First Drive"
NRMA Motoring and Services
flic.kr/p/d1bozj

"The braking distance for a 2012 Chrysler 300C to slow down from 31 m/s to a complete stop is 50.3 m. Assume that the acceleration is constant as the car slows down to a stop, and always points in the opposite direction as its velocity."

From the statement of this problem, determine whether the values of these kinematic quantities are known/given or are unknown/undetermined (without solving the problem numerically).
(Only correct responses shown.)

Final horizontal position x (initial horizontal position x₀ assumed to be 0): known/given. [86%]
Initial horizontal velocity v_0x: known/given. [89%]
Final horizontal velocity v_x: known/given. [82%]
Horizontal acceleration a_x: unknown/undetermined. [75%]
Final time t (initial time t₀ assumed to be 0): unknown/undetermined. [75%]

For the Chrysler 300C, the horizontal distance traveled is __________ the magnitude of the horizontal displacement.

less than.	** [2]
equal to.	******************************** [32]
greater than.	******** [8]
(Unsure/guessing/lost/help!)	** [2]

"Leichtathletik WM 2009 Berlin"
André Zehetbauer
flic.kr/p/6RmNQn

"Jamaican sprinter Usain Bolt holds the world record for the 100 m sprint, covering that (straight-line) distance in 9.58 s in Berlin, 2009. Assume that his acceleration starting from rest to when he crosses the finish line is constant, and always points in the same direction as its velocity."

From the statement of this problem, determine whether the values of these kinematic quantities are known/given or are unknown/undetermined (without solving the problem numerically).
(Only correct responses shown.)

Final horizontal position x (initial horizontal position x₀ assumed to be 0): known/given. [95%]
Initial horizontal velocity v_0x: known/given. [52%]
Final horizontal velocity v_x: unknown/undetermined. [52%]
Horizontal acceleration a_x: unknown/undetermined. [77%]
Final time t (initial time t₀ assumed to be 0): known/given. [95%]

For Usain Bolt, the horizontal distance traveled is __________ the magnitude of the horizontal displacement.

less than.	*** [3]
equal to.	**************************** [28]
greater than.	*********** [11]
(Unsure/guessing/lost/help!)	** [2]

"6 kJ Portable Pneumatic Catapult"
UAV Factory
uavfactory.com/product/21

"A portable pneumatic catapult is able to launch a Penguin B unmanned aerial vehicle (UAV) from rest to a final speed of 23 m/s along a 4.0 m rail. Assume that the rail is horizontal, and that acceleration of the UAV starting from rest to when it is launched is constant, and always points in the same direction as its velocity."

From the statement of this problem, determine whether the values of these kinematic quantities are known/given or are unknown/undetermined (without solving the problem numerically).
(Only correct responses shown.)

Final horizontal position x (initial horizontal position x₀ assumed to be 0): known/given. [61%]
Initial horizontal velocity v_0x: known/given. [82%]
Final horizontal velocity v_x: known/given. [89%]
Horizontal acceleration a_x: unknown/undetermined. [61%]
Final time t (initial time t₀ assumed to be 0): unknown/undetermined. [84%]

For the UAV, the horizontal distance traveled is __________ the magnitude of the horizontal displacement.

less than.	**** [4]
equal to.	************************ [24]
greater than.	******** [8]
(Unsure/guessing/lost/help!)	******** [8]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I am still a little unsure of the difference between horizontal distance and the magnitude of the horizontal displacement? I believe they are the same as long as the object is moving in one direction but not confident." (You are correct.)

"For the Usain Bolt 100-m sprint question, are we assuming that he's running on a straight or curved track? If it's curved, wouldn't that make the displacement magnitude smaller than the total distance traveled?" (If the sprint were along a curved track, then yes, the displacement magnitude smaller than the total distance traveled. However, a 100-m sprint is usually along a straight section of track, in which case the displacement magnitude would be equal to the total distance traveled.)

"When a problem says to assume acceleration is constant, does that mean it is 0?" (Not necessarily. When acceleration is zero, it is constant. But acceleration can be a constant non-zero value as well.)

"This is very basic stuff, but it is very important in order to do well in any type of physics."

"Can you please go over one of these questions including kinematic quantities in class." (We will.)

"Will Quiz 2 be structured in roughly the same way as the 'chain of pain' worksheet done in class last Wednesday?" (Yes, for several questions, the rest will be on kinematic equations and on free fall, which we will cover this week.)

"What is the best way to study for your tests?" (Study questions from old quizzes and midterms. Which is every example done in class, the majority of homework problems, and also the practice quizzes from last semester.)

Online reading assignment: motion

Physics 205A, fall semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on the reading textbook chapters and previewing a flipped class presentation on (constant acceleration) motion.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Using derivatives and integrals to move left or right on the chain of pain, respectively."

"From what I was able to deduce, the reading is about the relationship between acceleration, velocity, and motion. When you follow the charts given they show their relationship by tangents and chords (and areas)."

"The concept of acceleration--how it correlates to what we've already learned with velocity and displacement. With a positive acceleration headed in the same direction as the velocity, the velocity increases, resulting in the object moving faster. However with a negative acceleration pointed in the opposite direction, the object slows down resulting in a smaller velocity."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I think the kinematic equations were a lot to process. It made sense, but I need to get more familiarized with them."

"I don't understand how chord slopes work and what information it is telling me. I also don't get what number would be the chord slope."

"The graphical relations are confusing at the moment but will hopefully be clarified once I see some of these graphical relations in action. When I'll need to use what equation will take some studying."

"I don't fully understand the operations that are embedded in our non-calculus 'chain of pain.' I'm confused on how they all connect."

"Memorizing all the equations. I have little practice or interactions with these equations and the key to learning it would be to have a visual connected with every part of the equation so I can learn by logic and not memorization. Also lost on the slopes."

Briefly describe the difference(s) between a chord slope and a tangent slope on a graph.

"A chord slope is a straight line that connects two points on a curve. A tangent slope touches the line at only one point."

"A tangent line is slope of a line from a single point on a curved line and a chord slope is the line between two points on the curve."

"Chord slopes are for average values and tangent slopes are for instantanious."

"I honestly don't understand these concepts enough to explain."

Mark the level of your exposure to (basic calculus) concepts of derivatives/integrals.

None at all.	********** [12]
Slight.	******* [7]
Some.	******** [8]
A fair amount.	************* [13]
A lot.	*** [3]

Indicate how each of these quantities are determined from kinematic graphs.
(Only correct responses shown.)

Displacement ∆x: area under a v_x(t) graph. [58%]
Position x: (None of these choices.) [40%]
Change in (instantaneous) velocity ∆v_x: area under an a_x(t) graph. [51%]
(Instantaneous) velocity v_x: tangent slope of an x(t) graph. [65%]
Average velocity v_x,av: chord slope of an x(t) graph. [60%]
(Instantaneous) acceleration a_x: tangent slope of a v_x(t) graph. [56%]
Average acceleration a_x,av: chord slope of a v_x(t) graph. [58%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"What is the most important thing to understand from this homework?" (Knowing what to do with a graph, and how to do it (calculating areas, chord slopes, or tangent slopes, i.e. the "chain of pain").)

"I'm a little confused on when to use m/s and m/s². Is m/s used only with velocity and m/s² only with acceleration?" (Yes.)

"Why have a chart that sounds and looks torturous?"

"The chain of pain is so daunting at first but if you stare at it long enough it kind of starts to make sense, as long as you can see the system and you know the variables."

"I am finding the 'chain of pain' very confusing. Can you please lecture on this in class."

"I'm confused by 'v_av,x.' Is that the average velocity based off of the displacement value of x?" (Yes, it is the average horizontal velocity.)

"Will we be making or looking at graphs during the next lab?" (Yes, next lab will be an introduction to graphs in general (using Excel), and the following two labs will have you generating velocity versus time graphs generated from video tracking software, or from ultrasound motion detectors.)

"Do we have to memorize all these formulas and the kinematic graphs?" (All of the equations will be given to you. However, the relationships between the graphs (areas, chord slopes, and tangent slopes, i.e. the "chain of pain") is something you have to memorize yourself.)

"How do you solve kinematics equations that have more than one missing variable? Would you use substitution?" (Yes. You would need as many equations as you have missing variables.)

"This class is beginning to concern me."

"Hopelessly lost :("

Physics midterm question: position of vertically-launched ball

Physics 205A Midterm 1, fall semester 2018
Cuesta College, San Luis Obispo, CA

A Physics 205A student slings a ball straight upwards. The v_y(t) graph of this ball is shown at right, starting from when the ball was released at y = 0 at t = 0. Neglect air resistance. Choose up to be the +y direction. At t = 6 s, discuss why the ball is at a position higher than its release point. Explain your reasoning using the properties of velocity, position, distance traveled, and/or displacement.

Solution and grading rubric:

• p:
  Correct. Supports claim that the ball is still above its release point at t = 6 s by discussing at least one of the following explanations:
  1. displacement is the bounded area between the velocity function and the time axis, and since there is a greater bounded area above the time axis (corresponding to a positive displacement for t = 0 to 4 s) than the bounded area below the time axis (corresponding to a negative displacement for t = 4 s to 6 s), the ball has traveled farther up from its starting point to its highest height, than traveling downwards from its highest height to its final position at t = 6 s; or
  2. the ball slows down from an upwards velocity of +40 m/s at t = 0 to zero velocity at its highest point at t = 4 s, and from symmetry, the ball should fall back down to its starting point with a downwards speed of –40 m/s at t = 8 s, such that the ball is still somewhere above its starting point at t = 6 s; or
  3. uses kinematic equations for constant motion to show that the final position at t = 6 s is still positive.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01g4iN
p: 24 students
r: 5 students
t: 21 students
v: 8 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1414):
Another sample "p" response (from student 3691):

Physics midterm question: net force of two opposite forces on accelerating object

Physics 205A Midterm 1, fall semester 2018
Cuesta College, San Luis Obispo, CA

A physics question on an online discussion board[*] was asked and answered:

P-dog: If there are only two opposing forces acting on an accelerating object, is it possible for the net force to ever be larger than either of those two forces?
OSG: No.

Discuss why this answer is correct, and how you know this. Explain your reasoning using free-body diagram(s), the properties of forces, and Newton's laws.

[*] answers.yahoo.com/question/index?qid=20180916184605AASRFkI.

Solution and grading rubric:

• p:
  Correct. Complete free-body diagram, and discusses/demonstrates:
  1. the net force is the vector addition of all forces (in this case, only two forces) acting on the same object; and
  2. since these two forces are opposite in direction, one force must be larger than the other in order for the object to be accelerating (Newton's second law); then
  3. the net force cannot be more than the larger of the two forces acting on the object, as the net force is the difference of the magnitudes of these two forces (i.e., the magnitude of the larger force minus the smaller magnitude force). (It is also possible that the net force could be smaller than both of the two forces acting on the object.)
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying Newton's laws to a free-body diagram.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic application of Newton's laws to the forces on a free-body diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01g4iN
p: 33 students
r: 11 students
t: 2 students
v: 10 students
x: 1 student
y: 0 students
z: 1 student

A sample "p" response (from student 1842):
Another sample "p" response (from student 1996):

Physics midterm question: stuck or unstuck crate?

Physics 205A Midterm 1, fall semester 2018
Cuesta College, San Luis Obispo, CA

A force is applied to the right on a 5.0 kg crate on a horizontal floor that has a static friction coefficient µ_s = 0.35. Initially the crate is stationary. Discuss whether or not the crate will remain stationary if the magnitude of the applied force is slowly increased from zero up to a value just below the magnitude of the normal force of the floor on the crate. Explain your reasoning using free-body diagram(s), the properties of forces, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Complete free-body diagram, and discusses/demonstrates:
  1. the crate has two vertical forces acting on it:

     Weight force of Earth on crate (m·g = 49 N, downwards),
     Normal force of table on crate (49 N, upwards),

     and since there is no vertical motion, these two vertical forces must be equal in magnitude due to Newton's first law;
  2. the maximum amount of static friction force that must be overcome in order to unstick the crate is µ_s⋅N = (0.35)·(49 N) = 17 N; and
  3. since the applied force is slowly increased is "slowly increased from zero up to a value just below the magnitude of the normal force of the floor on the crate" (from 0 N up to 49 N), then the applied force will eventually be greater than maximum static friction force, such that the crate will unstick (and begin to accelerate to the right).
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some substantive attempt at analyzing how/if the maximum static friction force is overcome using Newton's laws and a free-body diagram.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at analyzing how/if the maximum static friction force is overcome using Newton's laws and a free-body diagram.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic attempt at using Newton's laws and a free-body diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01g4iN
p: 20 students
r: 7 students
t: 7 students
v: 12 students
x: 11 students
y: 0 students
z: 0 students

A sample "p" response (from student 6577):