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 problem: skateboard-launched rubber duck toy

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

"WRECKING BALL Vs. SEESAW from 45m! How High Will the Watermelon Go?"
How Ridiculous
youtu.be/1quHlRJLtgM

Brett Stanford, Derek Herron and Scott Gaunson for the "How Ridiculous" YouTube channel dropped a heavy ball on one end of a skateboard to launch a rubber duck toy from the other end. Video analysis shows that the toy was launched at an angle of 61° from the horizontal, and took 3.2 s from the moment it was launched from the ground to land back down on the ground. Determine the horizontal distance along the ground from where it was launched to where it landed. Neglect air resistance, and treat the toy as a point object that started on the ground. Show your work and explain your reasoning using properties of projectile motion.

[*] youtu.be/1quHlRJLtgM?t=335.

Solution and grading rubric:

• p:
  Correct. From the time of flight t = 3.2 s, solves for the initial vertical velocity component v_0y = +16 m/s. Next, using the launch angle of elevation θ = 61° finds the initial horizontal velocity component v_0x = +8.7 m/s, and subsequently uses that value and the time of flight t = 3.2 s to solve for the final horizontal position x = +28 m.
• r:
  Nearly correct, but includes minor math errors. At least successfully solves for the vertical v_0y and/or horizontal v_0x components of the initial velocity vector.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least some systematic attempt at using kinematic equations for projectile motion. May have made one or more erroneous assumptions about certain values, such as setting the final velocity components v_x = 0 and or v_y = 0, but still methodically solves for a (wrong) value of v_0y, and then (somehow) solves for a (wrong) value of v_0x using trigonometry to find a (wrong) value for the final horizontal position x.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at systematic use of kinematic equations for projectile motion.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at kinematic equations for projectile motion.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01duCk
p: 15 students
r: 4 students
t: 9 students
v: 21 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 5832):
Another sample "p" response (from student 2342):

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

Online reading assignment: speed and velocity

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 presentation on displacement, distance traveled, and average/instantaneous speed/velocity.


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 understood the unit conversions very well. This may be because I have a large amount of practice from chemistry for unit conversions."

"I learned the differences between displacement and distance traveled and when to use them in certain situations. I also learned the formulas and how to calculate average speed average velocity and instantaneous velocity."

"Essentially, displacement acts as a measurement of the straight-line distance between point A and B while distance traveled encompasses all of the paths made outside of the straight line--or, how it got there."

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 understand the formulas like average speed is distance divided by time but doing more problems in class to make myself more familiar and less confused would be helpful. I am also slightly confused with the symbols."

"Making the full connection between average speed, and average velocity, has me confused some with the magnitude vector and using exact distance now how to use them correctly. I also am confused on how to use instantaneous velocity and speed correctly."

"At first, instantaneous velocity was confusing for me as it raised the question, "what value is deemed small enough--in both displacement distance and time--to be considered for the instantaneous velocity formula?" However, upon further reading--actually right under the formula in the slide--you state it would result in a value APPROACHING instantaneous velocity but not actually instantaneous velocity. Basically, the more precise stuff comes later. Possibly, way later. Maybe never. You tell me."

"Limits are confusing both in calculus and physics."

"There wasn't much confusing as I have taken a previous physics course."

Briefly describe how you would walk along a straight, level road such that your distance traveled would be longer than your displacement.

"If you were walking a straight line and walked back a couple of yards, then continued down the road, your distance traveled would be greater than your displacement."

"Distance could be greater than displacement, if you dropped something and had to return to pick it up and then continue in the original direction. Or possibly saw something interesting in the distance say to the right of travel direction, and walked over to see the mystical object and then continued back to the original direction. This would make the distance longer than the overall displacement value, I think?"

"Walk along straight road from initial starting point A to ending point B, but before reaching point B you turn around and walk towards point A. The total distance walked is greater than your displacement once you walk in the opposite direction."

"You would walk forward for a while then turn around or walk backwards."

In general, average speed will be __________ the magnitude of average velocity.

less than.	**** [4]
equal to.	**************** [16]
greater than.	***************** [17]
(More than one of the above choices.)	********* [9]
(None of the above choices.)	[0]
(Unsure/guessing/lost/help!)	** [2]

In general, (instantaneous) speed will be __________ the magnitude of (instantaneous) velocity.

less than.	[0]
equal to.	****************************** [30]
greater than.	[10]
(More than one of the above choices.)	*** [3]
(None of the above choices.)	[0]
(Unsure/guessing/lost/help!)	***** [5]

In general, which of the following quantities could be negative?

Average velocity.	************ [12]
Average speed.	[0]
(Instantaneous) velocity.	* [1]
(Instantaneous) speed.	[0]
(More than one of the above choices.)	***************************** [29]
(None of the above choices.)	* [1]
(All of the above choices.)	*** [3]
(Unsure/guessing/lost/help!)	** [2]

An odometer measures an object's:

displacement.	* [1]
distance traveled.	********************************************** [46]
(instantaneous) velocity.	* [1]
(instantaneous) speed.	[0]
(Unsure/guessing/lost/help!)	[0]

A speedometer measures an object's:

displacement.	** [2]
distance traveled.	[0]
(instantaneous) velocity.	** [2]
(instantaneous) speed.	******************************************** [44]
(Unsure/guessing/lost/help!)	[0]

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

Is velocity the only quantity considered a vector?" (Of all the quantities we've considered so far (displacement/distance traveled, average velocity/speed, instantaneous velocity/speed), displacement, average velocity, and instantaneous velocity are all vectors, as they have magnitude and direction. Distance traveled, average speed, and instantaneous speed are all not vectors, as they only have (a positive) magnitude, and have no specified direction.)

"OH WAIT. I think it might be coming back to me from trigonometry. Is it that velocity is basically speed with a direction? It's pretty much speed with a direction, right? This is all confusing for me but perhaps it will make sense after class."

"I'm sorry If some of the answers are incorrect, I'm currently at a Starbucks and they're kicking us out due to it being close to closing time!"

"What is the difference between average and instantaneous speed?"

"Can you please review instantaneous speed versus velocity in class?"

"I just need more time with the instantaneous speed and velocity. The average speed and velocity I'm comfortable with."

"My question is in regards to the quiz questions on the main page. Will we be provided with conversion factors on quizzes and tests?" (Yes, as needed.)

"How do you handle quizzes with DSPS students? Since they are given at the beginning of class." (Arrangements would be made with DSPS to take the quiz before class. Midterms can be taken anytime the day of class.)

"Was the first week of school everything you ever dreamed of?" (Yes. But every first week of school is like that. What happens afterwards, well, that's a different story.)

"I feel like in physics where I struggled in the most what with over thinking when it came to anything with a number but what I found helped we was reading the chapter beforehand even if it was a glance or in class."

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 problem: plausible cliff height for ATV jump

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

In 2005, Chip Gaines reportedly drove a four-wheeled all-terrain vehicle over an embankment at the edge of a cliff, and became airborne:

I gunned it and launched that four-wheeler straight off the other side of the hill—over a sheer cliff that dropped a good twenty feet to the ground... In a matter of two seconds, the four-wheeler and I...face-planted into the dirt from nearly twenty feet up... And that's how I wound up with this awesome scar.[*]

While Chip Gaines claims that the cliff was 20 ft high (6.0 m), his wife Joanna Gaines recalls that the cliff was only 10 ft high (3.0 m).

Determine which cliff height (6.0 m or 3.0 m) was more plausible for Chip Gaines to be airborne for two seconds after launching himself on his four-wheeler (presumably a 2003 Kawasaki KVF 360 4⨉4[**]) with a speed of 38 mph (17 m/s) at an angle of 30° above the horizontal. Neglect air resistance, and treat Chip Gaines as a point object. Show your work and explain your reasoning using properties of projectile motion.

[*] Chip Gaines, Capital Gaines: Smart Things I Learned Doing Stupid Stuff, W Publishing (2017), pp. 44-47.
[**] kawasakimotorcycle.org/forum/kawasaki-atv-mule/30810-top-speed-360-a.html.

Solution and grading rubric:

• p:
  Correct. From the initial speed of v₀ = 17 m/s and direction of 30° above the horizontal, finds the y-component of initial velocity v_0y = v₀·sinθ = +8.5 m/s; applies projectile motion equations to determine that at t = 2 s, Chris Gaines would be at a final height of y = –2.6 m (thus 2.6 m below his starting point of y₀ = 0), thus making Joanna Gaines' estimate for the cliff height (3.0 m) more plausible that Chris Gaines' estimate of 6.0 m. May instead started with y = –3.0 m and y = –6.0 m and used the quadratic equation to solve for the expected times to reach the bottom of these cliffs, and found that the time to reach a final position of y = –3.0 m is closer to the given t = 2 s.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least some systematic attempt at using kinematic equations for projectile motion.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at systematic use of kinematic equations for projectile motion.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at kinematic equations for projectile motion. Primarily applies trigonometry to find distances rather than velocity components.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01g4iN
p: 31 students
r: 8 students
t: 8 students
v: 3 students
x: 7 students
y: 0 students
z: 1 student

A sample "p" response (from student 0517):

Physics quiz question: distance traveled vs. displacement magnitude

Physics 205A Quiz 3, fall semester 2018
Cuesta College, San Luis Obispo, CA

A Physics 205A student throws a basketball with an initial velocity vector that has x- and y-components:

v_0x = +5.5 m/s,
v_0y = +4.2 m/s.

Neglect air resistance. From being launched to reaching the highest height of its trajectory, the basketball's distance traveled will be __________ the magnitude of its displacement.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

For projectile motion, the distance traveled is measured along its curved trajectory, and is longer than the magnitude of the displacement, which is the length of the straight-line vector that starts from the release point, and ends at the highest point of its trajectory.

(Response (A) can never be true for any possible path taken by an object. Response (B) can only be true for an object traveling along a straight-line with no reversals in direction.)

Sections 70854, 70855
Exam code: quiz03pRH5
(A) : 4 students
(B) : 12 students
(C) : 40 students
(D) : 0 students

Success level: 71%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53

Physics quiz question: displacement and/or distance traveled?

Physics 205A Quiz 2, fall semester 2018
Cuesta College, San Luis Obispo, CA

The v_x(t) graph of a Physics 205A student walking along a straight line is shown at right. The student started at x = 0 at t = 0. The shaded area is the student's __________ for the time interval 4 s ≤ t ≤ 8 s.
(A) displacement.
(B) distance traveled.
(C) (Both of the above choices.)
(D) (Neither of the above choices.)

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.

Sections 70854, 70855
Exam code: quiz02HwRd
(A) : 16 students
(B) : 10 students
(C) : 20 students
(D) : 6 students

Success level: 38%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80

Online reading assignment: speed and velocity

Physics 205A, fall semester 2018
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 presentation on displacement, distance traveled, and average/instantaneous speed/velocity.


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.

"There are two types of paths: distance traveled (always positive) which is how far someone travels regardless of direction, and displacement (positive or negative) which is the straight-line distance someone travels from initial starting point to final ending point."

"that traveled distance is always greater than displacement. Speed deals with distance while velocity deals with displacement."

"The difference between distance and displacement--I know that distance will always be positive and measures all of the distance traveled in either direction or back and forth. On the other hand, displacement can be positive or negative and represents a straight line from the starting to end point an object traveled."

"That direction of motion isn't factored while measuring distance and speed while it is important when calculating displacement and 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.

"When to use the symbols given for each definition, and how I would use them. Like initial position, length, displacement, average velocity, instantaneuos velocity, etc."

"The relationships between average velocity and average speed."

"I didn't really understand the instantaneous velocity. How is it that we record multiple different positions of an object? And what exactly is approachng zero? i don't understand how to apply this final concept of the reading."

"I was a little frustrated that instantaneous speed was mentioned, but it was not explained. Maybe instant speed is equal to instant velocity? I say this because perhaps instant speed is equal to small change in distance traveled divided by small change in time. And small change in distance traveled equals small change in displacement, and the time interval would be the same. But I think instant velocity has a direction, whereas instant speed does not."

"The concepts of instantaneous velocity and instantaneous speed."

"I would like a review on instantaneous velocity vs. instantaneous speed. It would help just hearing it be talked about and explained so I can see how you explain it. I know some from calculus."

Briefly describe how you would walk along a straight, level road such that your distance traveled would be longer than your displacement.

"You walk your dog one mile to the store and one mile back to your house. Displacement is zero. Distance traveled is two miles."

"Walking back and forth along the straight road would allow the distance traveled to be greater than the displacement."

"Walk forwards and then also walk backwards because no matter the direction(s) traveled, distance is always accounted for."

"If you were to walk on a curved path from point A to point B, as opposed to a straight line, your distance would be longer than your displacement. Displacement is a vector measuring the shortest distance between point A and point B. Whereas distance is the actual path that was taken from point A to point B."

"Unless you are robotically programmed, I don't see human kind taking the shortest possible path on a straight road because of factors like crossing the road and maybe going left or right a little too much for some steps."

"Your distanced traveled would be longer if you went off the straight line, maybe if you did a loop and then continued on."

In general, average speed will be __________ the magnitude of average velocity.

less than.	*** [3]
equal to.	*********** [11]
greater than.	******************* [19]
(More than one of the above choices.)	****** [6]
(None of the above choices.)	* [1]
(Unsure/guessing/lost/help!)	***** [5]

In general, (instantaneous) speed will be __________ the magnitude of (instantaneous) velocity.

less than.	* [1]
equal to.	************************ [24]
greater than.	******* [7]
(More than one of the above choices.)	*** [3]
(None of the above choices.)	[0]
(Unsure/guessing/lost/help!)	********** [10]

In general, which of the following quantities could be negative?

Average velocity.	*********** [11]
Average speed.	[0]
(Instantaneous) velocity.	**** [4]
(Instantaneous) speed.	[0]
(More than one of the above choices.)	************************ [24]
(None of the above choices.)	[0]
(All of the above choices.)	* [1]
(Unsure/guessing/lost/help!)	***** [5]

An odometer measures an object's:

displacement.	** [2]
distance traveled.	****************************************** [42]
(instantaneous) velocity.	[0]
(instantaneous) speed.	[0]
(Unsure/guessing/lost/help!)	* [1]

A speedometer measures an object's:

displacement.	** [2]
distance traveled.	* [1]
(instantaneous) velocity.	* [1]
(instantaneous) speed.	***************************************** [41]
(Unsure/guessing/lost/help!)	[0]

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

"Going over the multiple-choice definition questions above would be much appreciated. Thank you!"

"Confused on average speed, average velocity, snd instantaneous velocity. Examples in class would be recommended."

"Will we need to know conversions (for example, 1 cm = 2.54 in) or will you give us a sheet of conversions for the tests?" (I will always give you the conversions that are needed to solve each question. You don't need to memorize everything, other than basic time stuff (1 min = 60 s, 1 h = 60 min, 1 day = 24 h). If you can't remember those, well, you can still ask me.)

"I would really appreciate an embedded tutor." (I would, too, but my embedded tutors from last year moved away over this summer. I've submitted a list of 10-15 more candidates for the Learning Resource Center to follow up on, so we'll see.)

"If labs are completed early with time to spare, do you ever take time to go over lecture material that is still confusing to students?" (Essentially I'm paid for the entire three hours of lab, so after you finish your lab work, feel free to stick around in the time remaining and ask me questions from lecture.)

"If you add 66 + 92 + 95 = 201, should it be 201 or 200 for significant figures or considering there is no decimal place would it just be 201?" (Since you are adding these numbers, and all of them have zero decimal places, then the answer (201) will also have zero decimal places. Note that the answer now has a different amount of significant figures than any of the numbers that went into it; this is typical of the addition/subtraction rule, where you have to keep track of the least number of decimal places (and not significant figures), and as a result may have a different number significant figures for your final answer.)

"When you are adding and one number is in scientific notation and the other is not you have to change scientific notation back? For example, if you had (4.576×10³ + 350), you would have to change 4.576×10³ to 4,576?" (Yes, when applying the addition/subtraction rule, all numbers must have the same power of 10, whether you would express them as 4,576 + 350 = 4,926; or 4.576×10³ + 0.350×10³ = 4.926×10³.)

Physics midterm question: comparing distances traveled

Physics 205A Midterm 1, fall semester 2017
Cuesta College, San Luis Obispo, CA

The x(t) graph of a Physics 205A student walking along a straight line is shown at right. The student started at x = 0 at t = 0. Discuss why the student traveled a farther distance from t = 0 to t = 7 s than the distance traveled from t = 7 s to t = 10 s. Explain your reasoning using the properties of position, distance traveled, and displacement.

Solution and grading rubric:

• p:
  Correct. Supports claim that student traveled a farther distance from t = 0 to t = 7 s than from t = 7 s to t = 10 s by discussing:
  1. distance traveled counts both forwards and backwards motion, such that from t = 0 to t = 7 s the student traveled a total distance of 3 m (2 m in the forwards direction, then 1 m in the backwards direction); compared to
  2. the distance traveled by the student from t = 7 s to t = 10 s is 2 m (always in the forward direction).
• 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. At least discussion demonstrates general understanding of distinction between distance traveled and displacement, but does not compare differences in distances traveled for the two time intervals.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May compare areas, slopes, elapsed times, average speeds and/or average velocities.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm01mOoL
p: 25 students
r: 3 students
t: 10 students
v: 15 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 2030):

Physics midterm problem: world-record washing machine throw

Physics 205A Midterm 1, fall semester 2017
Cuesta College, San Luis Obispo, CA

"Washing Machine Throwing Showdown"
Guinness World Records
youtu.be/YC0oj7BcWiI

In 2017, Zydrunas Savickas set a world record throwing a 46 kg (101 lb) washing machine that landed a horizontal distance of 4.13 m from its starting position atop his head. Savickas' height is 1.91 m, and the washing machine was airborne for 1.84 s starting from just off the top of his head to just before hitting the ground[*].

Find both the horizontal and vertical components (v_0x, v_0y) of the initial velocity vector for the washing machine, as it was thrown and released from just above the top of Savickas' head. Neglect air resistance, and treat the washing machine as a point object. Show your work and explain your reasoning using properties of projectile motion.

[*] Rachel Swatman, "Watch Game of Thrones Star Take on World’s Strongest Man Winner in Washing Machine Throwing Showdown" (January 13, 2017), guinnessworldrecords.com/news/2017/1/watch-game-of-thrones-star-take-on-world%E2%80%99s-strongest-man-winner-in-washing-machi-458290.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates:
  1. uses given values of t = 1.84 s and x = +4.13 m to solve for the initial (and constant) horizontal velocity v_0x (where t₀ = 0, x₀ = 0); and
  2. uses given values of t = 1.84 s and y = −1.91 m to solve for the initial vertical velocity v_0y (where t₀ = 0, y₀ = 0).
• r:
  Nearly correct, but includes minor math errors. May have intentionally or unintentionally used y = +1.91 m or y = 0 instead of y = −1.91 m.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has one initial velocity component correct, but other component has errors in addition to those listed in (r), such as setting v_y = 0 in y = (1/2)⋅(v_y0 + v_y)⋅t to solve for v_y0, or setting v_x = 0 in x = (1/2)⋅(v_0x + v_x)⋅t to solve for v_x0, etc.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized 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: midterm01mOoL
p: 20 students
r: 16 students
t: 12 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1956):

Physics quiz question: Skycycle X-2 average speed vs. magnitude of average velocity

Physics 205A Quiz 3, fall semester 2017
Cuesta College, San Luis Obispo, CA

"Evel Knievel's Skycycle"
Tennessee Dept. of Tourism
tnsjournal.com/entertainment/history-channel-museum-men-filming-sevierville/

Evel Knievel's Skycycle X-2 rocket ship was launched with an initial speed of 44 m/s at an angle of 56° above the horizontal[*]. Neglect air resistance, and treat the rocket as a thrown object. From being launched to reaching the highest height of its trajectory, the rocket ship's average speed will be __________ the magnitude of its average velocity.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

[*] James Vlahos, "The Devils And The Deep Blue Sky," popsci.com/article/technology/devils-and-deep-blue-sky, (September 24, 2014).

Correct answer (highlight to unhide): (C)

The average speed of the rocket ship is its distance traveled divided by elapsed time, while the magnitude of average velocity is given by the magnitude of displacement divided by elapsed time. For projectile motion, the distance traveled is measured along its curved trajectory, and is longer than the magnitude of the displacement, which is the length of the straight-line vector that starts from the ground, and ends at the highest point of its trajectory. Since the elapsed time for the rocket ship to travel from the start to finish is the same whether along the actual distance traveled or the straight-line displacement, the average speed of the rocket ship must be greater than the magnitude of its average velocity.

(Response (A) can never be true for any possible path taken by an object. Response (B) can only be true for an object traveling along a straight-line with no reversals in direction.)

Sections 70854, 70855
Exam code: quiz03T4uC
(A) : 6 students
(B) : 10 students
(C) : 32 students
(D) : 0 students

Success level: 59%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.63

Physics quiz question: comparing distances traveled

Physics 205A Quiz 2, fall semester 2017
Cuesta College, San Luis Obispo, CA

The x(t) graph of a Physics 205A student walking along a straight line is shown at right. The student started at x = 0 at t = 0. The student walks the greatest distance during the time interval(s):
(A) 0 ≤ t ≤ 3 s.
(B) 3 s ≤ t ≤ 7 s.
(C) 7 s ≤ t ≤ 10 s.
(D) (There is a tie.)

Correct answer (highlight to unhide): (D)

The positions of the student at different times can be immediately read off of this position versus time graph.

At t = 0, the student is located at x = 0 (this is also given in the statement of the problem). At t = 3 s, the student is then located at x = –2 m, such that the student traveled 2 m (in the negative direction) during the 0 ≤ t ≤ 3 s time interval.

At t = 3 s, the student is located at x = –2 m. At t = 7 s, the student is then located at x = –1 m, such that the student traveled 1 m (in the positive direction) during the 3 s ≤ t ≤ 7 s time interval.

At t = 7 s, the student is located at x = –1 m. At t = 10 s, the student is then located at x = –3 m, such that the student traveled 2 m (in the negative direction) during the 7 s ≤ t ≤ 10 s time interval.

Since the student traveled 1 m during the 3 s ≤ t ≤ 7 s time interval, but traveled 2 m during both the 0 ≤ t ≤ 3 s and the 7 s ≤ t ≤ 10 s time intervals, the most correct response is (D).

Sections 70854, 70855
Exam code: quiz02BjRn
(A) : 1 student
(B) : 19 students
(C) : 3 students
(D) : 32 students

Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.74

Online reading assignment: speed and velocity

Physics 205A, fall semester 2017
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 presentation on displacement, distance traveled, and average/instantaneous speed/velocity.


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.

"Distance traveled is always a positive quantity, secondary to it being the total distance an object travels regardless of its direction. While displacement can either be a positive or negative quantity depending on the direction the object traveled from its initial to final position."

"Distance is space traveled, always positive and displacement is the straight line from point a to point be, either positive or negative. speed is distance/time and velocity is displacement/time."

"I had a bit of a hard time understanding average velocity versus instantaneous velocity, but I think I understood it after a bit of thought. I realized that instantaneous velocity pertains to a specific instance in time. Since average velocity is the overall average it measures the displacement over a certain length of time."

"Average speed equals distance traveled divided by total time. It's always a positive quantity."

"Average speed and velocity are pretty easy to understand. Finding the average speed is done by dividing distance by elapsed time, such as miles per hour. And finding average velocity is done by dividing displacement by elapsed time."

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 struggling to keep significant figures straight between multiplication and addition. I tend to make simple mistakes and not have an answer that's even listed on the multiple choice."

"The differences between the different velocities and speeds kind of threw me for a loop. I'm not exactly sure about the magnitudes between them and when they are greater/less than or equal to one another."

"Something I struggled with was the instantaneous velocity and speed. Specifically how they were denoted and the equation used for instantaneous velocity and average velocity."

"I was a little confused on the difference between speed and velocity until I looked at the different examples and spoke the terms out loud."

"The most confusing points for me were what is the meaning of 'the magnitude' of anything like: average velocity, displacement, etc. Also, using some of the formulas in an actual problem might be helpful to understand the concepts better."

"I am truly lost on the instantaneous velocity. This is because the symbols used I am not familiar with and I'm just lost."

"I'm confused as to whether the speedometer would measure displacement or instantaneous speed."

"I'm still not completely following the instantaneous velocity. I understand it is the small displacement over the short time interval I just think discussing it further may make me more confident."

"There are no concepts presented in the reading that I do not understand."

Briefly describe how you would walk along a straight, level road such that your distance traveled would be longer than your displacement.

"You would walk forward and then walk backwards. This way your distance traveled is more than your displacement."

"If I walk straight 10 m then go back the same way 5 m , my displacement would be 5 m, however my distance traveled would be 15 m. Is that right?"

"Honestly I know why the distance would be longer than the displacement I just cannot find the right words to describe it."

"If you were walking along a straight road, your distance traveled would be longer than your displacement if you were to walk back and forth between the initial and final points."

In general, average speed will be __________ the magnitude of average velocity.

less than.	** [2]
equal to.	****************** [18]
greater than.	************** [14]
(More than one of the above choices.)	********** [10]
(None of the above choices.)	[0]
(Unsure/guessing/lost/help!)	**** [4]

In general, (instantaneous) speed will be __________ the magnitude of (instantaneous) velocity.

less than.	***** [5]
equal to.	********************************** [34]
greater than.	***** [5]
(More than one of the above choices.)	** [2]
(None of the above choices.)	[0]
(Unsure/guessing/lost/help!)	** [2]

In general, which of the following quantities could be negative?

Average velocity.	******* [7]
Average speed.	[0]
(Instantaneous) velocity.	* [1]
(Instantaneous) speed.	[0]
(More than one of the above choices.)	************************************ [36]
(None of the above choices.)	* [1]
(All of the above choices.)	*** [3]
(Unsure/guessing/lost/help!)	[0]

An odometer measures an object's:

displacement.	** [2]
distance traveled.	********************************************** [46]
(instantaneous) velocity.	[0]
(instantaneous) speed.	[0]
(Unsure/guessing/lost/help!)	[0]

A speedometer measures an object's:

displacement.	* [1]
distance traveled.	* [1]
(instantaneous) velocity.	* [1]
(instantaneous) speed.	********************************************* [45]
(Unsure/guessing/lost/help!)	[0]

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

"Not sure if this pertains to the preview for Monday or review for Wednesday!" (Well, both, actually.)

"How do we calculate the velocity for an object going in circular motion?" (Just worry about one-dimensional motion for now. #toosoon)

"Should we be starting a formula sheet to start memorizing, or will we be given formulas on quizzes/exams?" (Equations are given at the bottom of the archived quizzes, and on the last page of each in-class worksheet packet online. Note: there are no equations provided for the first quiz!)

"A review of the relationships between instantaneous speed/velocity vs. average speed/velocity would be helpful."

"Clarification on the relationships between magnitudes of average/instantaneous velocity/speed?"

Physics midterm question: maximizing Pokémon Go pokémon spawns

Physics 205A Midterm 1, fall semester 2016
Cuesta College, San Luis Obispo, CA

Pokémon Go is an application that runs on a smartphone that can track your location[*]:

According to the game's code, it will spawn a pokémon for you every five minutes if you're not moving. But if you're walking, they'll spawn faster. Walk in a straight line if you can. The game checks in and measures your location periodically. Walking around the same block over and over won't net you many pokémon spawns.

Determine whether Pokémon Go is programmed to reward you with "many pokémon spawns" by tracking your average speed, or tracking the magnitude of your average velocity. Explain your reasoning using the properties of position, distance traveled, displacement, speed, and velocity.

[*] Patrick Allan, "Two Walking Tips Every Pokémon Go Trainer Needs to Know" (August 4, 2016) lifehacker.com/two-walking-tips-every-pokemon-go-trainer-needs-to-know-1784847638.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates understanding of:
  1. distinction between magnitude of average velocity (displacement magnitude over the elapsed time), and between average speed (distance traveled over the elapsed time);
  2. specifically compares "walking around the same block over and over" versus walking "in a straight line" to argue that:
     1. "walking around the same block over and over" will result in a displacement magnitude that will be less than walking that same distance in a straight line, therefore Pokémon Go will "net you many pokémon spawns" by tracking your magnitude of average velocity, not your average speed; or
     2. "walking around the same block over and over" will result in the same distance traveled as walking that same distance traveled in a straight line, therefore Pokémon Go does not track your average speed in order to "net you many pokémon spawns."
• 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/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01br1Q
p: 38 students
r: 13 students
t: 5 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 3428):
Another sample "p" response (from student 6924):

Physics midterm problem: Snake River Canyon rocket jump

Physics 205A Midterm 1, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Stuntman successfully jumps Snake River Canyon"
KTVB Channel 7
ktvb.com/news/stuntman-successfully-jumps-snake-river-canyon/319488060

Stuntman Eddie Braun successfully completed a rocket jump over the Snake River in Idaho[*]. With a reported launch speed of 190 m/s at an angle of 55° above the horizontal, after traveling a horizontal distance of 740 m, the rocket reached a maximum height of 670 m above the ground.

Determine whether the reported 190 m/s was a plausible value for the launch speed (to within two significant figures). Neglect air resistance and the propulsion engine of the rocket (thus treating it as a thrown object). Show your work and explain your reasoning using properties of projectile motion.

[*] Loz Blain, "Eddie Braun Jumps the Snake River Canyon in an Evel Knievel-style Rocket Bike" (September 16, 2016), newatlas.com/eddie-braun-rocket-bike-jump-snake-river-knievel/45477/.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates:
  1. given maximum height y = +670 m at x = +740 m, calculates the initial speed (or initial velocity components);
  2. compares calculated initial speed (or initial velocity components) with reported value, and concludes there is a discrepancy of more than two significant figures.
  May instead discuss/demonstrate:
  1. holding other given values as fixed to find some other inconsistency in a reported value, such as time t to reach y = +670 m, time t to reach x = +740 m, or looks for a non-zero vertical velocity component v_y at y = +670 m, etc.;
  2. interprets that reported initial speed of 190 m/s is plausible in that the rocket jump would exceed the reported trajectory parameters and be "successful."
• r:
  Nearly correct, but includes minor math errors. At least successfully solves for the horizontal v_0x and vertical v_0y components of the initial velocity vector, but calculation and/or conclusion from finding/deducing a derived value to compare to a reported value is garbled.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors notwithstanding.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized 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, 73320
Exam code: midterm01br1Q
p: 29 students
r: 9 students
t: 6 students
v: 9 students
x: 3 students
y: 1 student
z: 0 students

A sample "p" response (from student 8321), finding that the reported initial velocity would result in a trajectory that would be higher and longer than the state values, and concludes that it is a plausible value in the sense that it would outdistance the (assumed) required trajectory:
Another sample "p" response (from student 3575), demonstrating that after the rocket has traveled a horizontal distance of 740 m, it is at a higher height than the stated maximum height of 670 m, and concludes that the reported initial velocity is a plausible value in that air resistance was not included in this analysis:
Yet another sample "p" response (from student 4566), showing a discrepancy in the vertical initial velocity component required in order for the rocket to reach its highest height of 670 m after traveling a horizontal distance of 740 m: