Distance-time Graph Research Articles

Graph plotting of 1-D motion in introductory physics education using scripts generated by ChatGPT 3.5

Introductory physics courses often necessitate students to graphically represent one-dimensional (1-D) motion and derive various physical parameters. Physical quantities are often solved by calculating either slope or the area under the graph. Instructors and students who do not have access to paid software must plot graphs by hand. This paper explores three introductory physics examples related to 1-D motion, and employs ChatGPT 3.5 to generate scripts that will produce graphs from raw data. It can generate scripts, based on accurate user inputs, in free programming languages like Python and/or GNU Octave to enable efficient graph plotting. Examples will be provided on calculating the slope of a distance–time graph and determining the area under a velocity–time graph. Given raw data, ChatGPT 3.5 may exhibit occasional inaccuracies when solving for physical parameters. However, user can communicate in English to modify the output. The author does not endorse the use of ChatGPT for academic misconducts such as assisting students to cheat in problem solving. Instead, ChatGPT is presented as a tool to enhance data visualisation for both instructors and students, which can potentially improve learning environments in introductory physics. This paper lays the groundwork for future initiatives, beyond the plotting of 1-D motion graphs, aiming to integrate artificial intelligence to assist more complex motion studies in physics learning environments.

Analysis of the Trajectory of Free-throws

This research paper delves into the intricate realm of free-throw shooting in basketball, combining advanced dataanalytics and artificial intelligence to dissect the trajectory of human-generated free-throws and induce the theoretically“perfect shot” by AI. This study aims to introduce the sport of basketball, provide valuable insights into the science ofbasketball shooting, and ultimately contribute to developing the skill of free-throw shooting. I used a real-life exampleof a free-throw shot to achieve this goal. Using the model, I molded a horizontal and vertical distance-time graph onthe coordinate plane to estimate the velocity at each second. By utilizing some physics kinematics, I was able to drawa free-body diagram of the basketball in motion and analyze the possible factors affecting its trajectory. Finally, as allmy research points toward the same goal, I hope to mathematically optimize the perfect trajectory to maximize thelikelihood of a perfect shot by an AI.

Effects of Fractures on Buildings and Road Construction: A Case Study of Area BZ, Ahmadu Bello University, Zaria, Nigeria

Structural collapse due to the absence of geophysical information has become a major concern in the construction and building industries today. In this research, we reported the effect of fracture on some selected buildings in Area BZ, Ahmadu Bello University, Zaria. Reflex W software was used to analyze the vertical and horizontal profiles of the subsurface features in two-dimensional (2D) tomography of seismically related regions. The data were collected using MK6 Terraloc seismograph. Seismic refraction method was used to obtain relevant information about the subsurface strata. The velocities of different layers were obtained from the distance-time graph to generate the tomography of the four profiles of 115 m distance each. Results revealed that there are fractures beneath the surface, starting from the depth of 10 m into the basement region as evident in the four (4) profiles with variations in the seismic velocities of 1652 to 2086 m/s and 2521 to 2955 m/s for given strata. The 2D tomography of the study area also revealed that the eastern parts of profiles 1-3 may not be safe for the erection of buildings and other structures without excavation, while profile 4 revealed high levels of structural deformation and it is recommended as a high-risk region that will not support engineering structure. We, however, recommend that further geophysical surveys should be carried out in the area, using Electrical Resistivity Tomography (ERT).

Validation of Newton’s second law using Arduino: STEM teaching material

The present work offers an experimental technique specially designed and employed to comprehend and teach the Newton’s second law and to overcome certain instructional difficulties. The apparatus is mainly comprised of two specifically designed toy cars, two force sensors, one distance sensor, a pulley, two pieces of gut, an Arduino microprocessor and an ordinary computer. Newton’s second law is experimentally validated by measuring, using the Arduino system, the accelerations from the distance–time graphs and by directly measuring the tension forces. The experimental results are also compared with theoretical calculations, indicating a reasonably good agreement. The designed apparatus can be employed as a Science Technology Engineering Mathematics teaching material within physics laboratories, to achieve enhanced understanding of Newton’s second law and dynamics.

How using comics can assist in determining the students’ learning of distance-time graphs

The art of teaching mathematics at all levels requires a lot of creativity and innovation from a teacher for the students to effectively grasp what they are taught. Teachers tend to devise various means always ensure that they understand the attention of a learner in mathematics lessons bearing in mind that some learners easily switch off in mathematics lessons. In this study, we explored how a teacher can effectively use comics while teaching upper secondary students the topic of Distance-Time Graphs. The research entails that problems exists among the mathematics areas where the students face a challenge in grasping the concepts they are taught and even lose concentration more quickly while the teacher is teaching thereby falsely conceptualising that mathematics is a difficult subject. The concepts involved in this paper are in concurrent to the existing literature that the use of comics is one of the ways to draw the attention of students while teaching them. An action research approach was adopted to determine whether students’ understanding of mathematics concepts in Brunei schools could be improved using comics. The problems that 38 Year 10 students encountered while learning Distance-Time Graphs have also been elaborated in this paper, and the methodology through which comics can be incorporated into the teaching and learning process in this area has also be shown for practical application in the Brunei secondary school. There is also an elaboration on how the research concerning the use of comics in teaching was conducted and how the hypothesis was analyzed and evaluated to have a positive outcome in the teaching and learning process.

Supporting primary school students\u2019 reasoning about motion graphs through physical experiences

Reasoning about graphical representations representing dynamic data (e.g., distance changing over time), including interpreting, creating, changing, combining, and comparing graphs, can be considered a domain-specific operationalization of the general twenty-first century skills of creative, critical thinking and solving problems. This paper addresses the issue of how these 21st century skills of interpreting and creating graphs can be supported in a six-lesson teaching sequence about graphing motion. In this teaching sequence, we focused on the potential of an embodied learning environment to facilitate the development of primary school students’ reasoning about motion graphs by having primary school students (9–11 years) ‘walk’ graphs in front of a motion sensor to generate distance-time graphs. We asked: How does students’ reasoning about graphing motion develop over a six-lesson teaching sequence within an embodied learning environment? Based on the collected data, we examined changes in students’ level of reasoning on graph interpretation and graph construction tasks using a repeated measurement design. Additionally, we present two teaching episodes showing instances of how perceptual-motor experiences during the lessons aided students’ reasoning about graphical representations of motion. Results show that students went from iconic understanding towards understanding in which they reasoned based on one or two variables when interpreting and constructing graphical representations of motion events. At these higher levels of reasoning these students showed understanding of modelling motion in line with the intended 21st century skills of generating, refining, and evaluating graphs.

The Elusive Slope

In understanding upper secondary school students’ interpretations of information in graphical representations of a distance–time graph and an ECG graph, little attention has been paid to the analysis of the condition of the conceptual development related to their utterances. Understanding this better can help improve the teaching of interpretations of information in graphical representations of different situations. This paper integrates results from 2 studies and 3 theoretical perspectives: Tall and Vinner’s theoretical perspectives on learning, Chi’s ontological perspectives on conceptual development and Friel’s theoretical perspectives on interpretation of graphical information. The findings provide evidence to support the conjecture that iconic interpretations could be stimulated and generated as a result of student categorisation of a distance–time graph as an event, when in fact the graph is being used to describe and communicate a process. The outcome further indicates that students found a resemblance between the ECG diagram and the periodic function of f(x) = sin(x).

Generalizing a categorization of students’ interpretations of linear kinematics graphs

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.Received 23 September 2015DOI:https://doi.org/10.1103/PhysRevPhysEducRes.12.010108This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasConcepts & principlesEpistemology, attitudes, & beliefsPhysics Education Research

초등학교 '물체의 속력' 단원 수업에서 교사와 학생이 느끼는 교수.학습곤란도 분석

The first purpose of this study is to distinguish difficult chapters in 'Speed of objects' chapter and find the factors which give difficulty to the teachers and students. Also, it attempts to compare the students' assessment scores with the degree of difficulty in teaching and also with the degree of difficulty in learning. This report is expected to help science teachers develop their PCK(Pedagogical Content Knowledge) for teaching the chapter professionally. 15 teachers who had taught the 'Speed of Objects' chapter and their 386 students took part in the survey to acquire information about the difficulties in teaching and learning. 386 students also received a test to examine their understandings of the chapter. The results of this study are as follow; First, the degree of teachers' and students' difficulty is only affected by the contents, and the degree of onerousness felt by teachers is higher than that of students. Second, The topics caused higher difficulty to teachers were 'Understanding the meaning of motion(2nd lesson)', 'Understanding the meaning and unit of speed(5th lesson)', 'Changing unit of speed(6th lesson)', 'Drawing a distance-time graph(7th lesson)', and 'Understanding the relative motion(10th). The topics that led higher difficulty to students were the contents of 5th, 6th, and 7th lessons. Third, the 'Speed of Objects' chapter can be divided into 4 types of difficulty according to the degree of teaching and learning; 'Strong difficulty', 'Learning difficulty', 'Weak difficulty', and 'Teaching difficulty'. Last, students showed low achievement to the tasks that were related with 'Strong difficulty' and 'Teaching difficulty'.

Categorization of first-year university students’ interpretations of numerical linear distance-time graphs

We have investigated the various approaches taken by first-year university students (n approximate to 550) when asked to determine the direction of motion, the constancy of speed, and a numerical value of the speed of an object at a point on a numerical linear distance-time graph. We investigated the prevalence of various well-known general graphing difficulties, such as graph-as-picture errors and slope-height confusion. We established that two-thirds of our students could determine the direction of motion with respect to a reference point, just under 80% could determine that the speed is constant, and just under 20% of our students could correctly determine the value of the speed; in the latter case, about half of the students divided the two coordinates. Three stable categories of correctly explaining the constancy of speed emerged from the data. We found that the reason given for determining that the speed of the object was constant did not correlate with successfully determining a value for the speed. We have established that technical difficulties such as determining the slope of any linear graph did not explain the poor performance. By comparing the answers to similar questions on water level versus time graphs, we were able to establish that context dependence and incorrect prior learning are likely to play a role. Post-test data are used to confirm the validity of the categorization and support the conclusion that being able to determine the slope of a y, x graph and having a correct qualitative understanding of a distance-time graph is not sufficient to correctly determine a value for the speed. DOI: 10.1103/PhysRevSTPER.9.010107

Time dilation in special relativity: an alternative derivation

It is shown that the well-known Lorentz formula for time dilation can be derived from a distance–time graph plotted for a spaceship communicating with Earth.

Calculation of contraction rates due to shrinkage in light-cured composites

Objective. To calculate the contraction rate that results from polymerization shrinkage in photo-cured resins. Method. Fourteen materials were irradiated in a previously developed instrument. This instrument uses measurements of deflection using a ‘bonded disk’ method. Six measurements were made on each material at 20±2 °C and 70±10% RH. Means and standard deviations were analyzed. Results. Shrinkage-strain and contraction rate are reported. Total shrinkage-strain for photo-polymerized resins (packable and flowable composites) varies between 1.65 and 4.16%. Both are ormocers. The contraction rate for photo-polymerized resins varies between 55.71 and 167.00 μm/min. Packable resins present a lower contraction rate than flowable resins. Significance. The distance–time graph is linear. The slope of this line is the average velocity. This concept was used to calculate the average contraction rate. The monomer percentage affects the contraction rate, because higher contraction rate means higher percentage of monomer. We can infer that contraction rate bears some relation to polymerization shrinkage.

Connecting Research to Teaching: Using Data-Collection Devices to Enhance Students' Understanding

While working with high school students at a Mathematics, Physics, and Advanced Technology Exploration Day, we observed an activity in which students tried to reproduce a distance-time graph by walking. They used a Calculator-Based Ranger (CBR) to collect data about their distance from a motion detector and to generate a distance-time graph in real time. During the activity, the students clearly did not understand the distance information that the given graph was conveying.

Changes in a preservice elementary teachers physics course

Preservice elementary teachers demonstrated the ability to read and interpret distance-time graphs before instruction. Posttest results suggested the new motion curriculum materials greatly improved students’ abilities to read and interpret velocity-time graphs. Despite conducting only one activity with acceleration, students also showed improvement with acceleration-time graphs. The instruction, which included MBL activities, improved the preservice teachers’ general conceptual understanding of these kinematic topics. Future research might include a means to better measure the cause for the conceptual change. Multiple factors played a role, including positive student attitudes toward using the computers, ability to make abstract concepts measurable and describable, and opportunities for frequent experimentation. The capabilities of MBLs changed the focus of the motion curriculum. An MBL’s capacity to quickly gather data and display it opens the door for a rich variety of activities. Developing new motion curriculum was enhanced with opportunities for experimentation and exploration made possible by this technology. The revision of the curriculum was rewarding and exciting for both the instructors and students. The students learned the content, saw an appropriate use of technology, and enjoyed using the computer. The instructors enjoyed exploring the topics using MBLs and became excited with the possibilities of further usage of MBLs. Using MBLs as the powerful tool they are, motion curriculum will continue to be revised, and the instructors will explore more effective ways of structuring the lessons with ways to better teach.