Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion

Teferi Mekit Dillo

doi:doi:10.11648/j.ijtam.20251104.12

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Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion

Teferi Mekit Dillo^*

Published in International Journal of Theoretical and Applied Mathematics (Volume 11, Issue 4)

Received: 22 October 2025 Accepted: 6 November 2025 Published: 9 December 2025

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Abstract

The study introduces the arithmetical framework to derive classical kinematic equations without using calculus and provides comparable equations for displacement. The proposed method establishes a direct correspondence between kinematic quantities—velocity, acceleration, displacement, and time—and the elements of arithmetic progressions. Conventional calculus-based methods encounter constraints when applied to systems that suffer from accuracy; thus, it indicates that there are alternate mathematical tools and methodologies. A carefully chosen arithmetic-based model is developed, treating time as continuous when studied as a sequence and as discrete when regarded in a series. Further, acceleration is modeled as a deterministic continuous quantity, while velocity and displacement follow deterministic discrete patterns. Through transforming physical correlations directly to arithmetic patterns, this framework provides alternative distance equations. Based on standard summation, a comparative analysis of a constant-acceleration problem shows that the arithmetic model predicts displacement (47 m) with about 9% more accuracy than the classical calculus result (43 m). This confirms that the method is physically valid, and it not only makes calculations easier and reduces mistakes, but it also helps people understand motion under uniform acceleration better and gives more accurate results than the calculus-based model. The results imply that the arithmetic framework offers a unified way to connect discrete and continuous motion and gives classical mechanics a new mathematical base that makes calculations clearer. Moreover, it offers fresh methods for dealing with increasingly simplifying complex physical phenomena and advancing conceptual clarity.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 11, Issue 4)
DOI	10.11648/j.ijtam.20251104.12
Page(s)	65-70
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Uniform Acceleration Motion, Distance, Velocity, Discrete, Arithmetical Pattern and Calculus

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Dillo, T. M. (2025). Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion. International Journal of Theoretical and Applied Mathematics, 11(4), 65-70. https://doi.org/10.11648/j.ijtam.20251104.12

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ACS Style

Dillo, T. M. Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion. Int. J. Theor. Appl. Math. 2025, 11(4), 65-70. doi: 10.11648/j.ijtam.20251104.12

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AMA Style

Dillo TM. Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion. Int J Theor Appl Math. 2025;11(4):65-70. doi: 10.11648/j.ijtam.20251104.12

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@article{10.11648/j.ijtam.20251104.12,
  author = {Teferi Mekit Dillo},
  title = {Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {11},
  number = {4},
  pages = {65-70},
  doi = {10.11648/j.ijtam.20251104.12},
  url = {https://doi.org/10.11648/j.ijtam.20251104.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20251104.12},
  abstract = {The study introduces the arithmetical framework to derive classical kinematic equations without using calculus and provides comparable equations for displacement. The proposed method establishes a direct correspondence between kinematic quantities—velocity, acceleration, displacement, and time—and the elements of arithmetic progressions. Conventional calculus-based methods encounter constraints when applied to systems that suffer from accuracy; thus, it indicates that there are alternate mathematical tools and methodologies. A carefully chosen arithmetic-based model is developed, treating time as continuous when studied as a sequence and as discrete when regarded in a series. Further, acceleration is modeled as a deterministic continuous quantity, while velocity and displacement follow deterministic discrete patterns. Through transforming physical correlations directly to arithmetic patterns, this framework provides alternative distance equations. Based on standard summation, a comparative analysis of a constant-acceleration problem shows that the arithmetic model predicts displacement (47 m) with about 9% more accuracy than the classical calculus result (43 m). This confirms that the method is physically valid, and it not only makes calculations easier and reduces mistakes, but it also helps people understand motion under uniform acceleration better and gives more accurate results than the calculus-based model. The results imply that the arithmetic framework offers a unified way to connect discrete and continuous motion and gives classical mechanics a new mathematical base that makes calculations clearer. Moreover, it offers fresh methods for dealing with increasingly simplifying complex physical phenomena and advancing conceptual clarity.},
 year = {2025}
}

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TY  - JOUR
T1  - Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion
AU  - Teferi Mekit Dillo
Y1  - 2025/12/09
PY  - 2025
N1  - https://doi.org/10.11648/j.ijtam.20251104.12
DO  - 10.11648/j.ijtam.20251104.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 65
EP  - 70
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20251104.12
AB  - The study introduces the arithmetical framework to derive classical kinematic equations without using calculus and provides comparable equations for displacement. The proposed method establishes a direct correspondence between kinematic quantities—velocity, acceleration, displacement, and time—and the elements of arithmetic progressions. Conventional calculus-based methods encounter constraints when applied to systems that suffer from accuracy; thus, it indicates that there are alternate mathematical tools and methodologies. A carefully chosen arithmetic-based model is developed, treating time as continuous when studied as a sequence and as discrete when regarded in a series. Further, acceleration is modeled as a deterministic continuous quantity, while velocity and displacement follow deterministic discrete patterns. Through transforming physical correlations directly to arithmetic patterns, this framework provides alternative distance equations. Based on standard summation, a comparative analysis of a constant-acceleration problem shows that the arithmetic model predicts displacement (47 m) with about 9% more accuracy than the classical calculus result (43 m). This confirms that the method is physically valid, and it not only makes calculations easier and reduces mistakes, but it also helps people understand motion under uniform acceleration better and gives more accurate results than the calculus-based model. The results imply that the arithmetic framework offers a unified way to connect discrete and continuous motion and gives classical mechanics a new mathematical base that makes calculations clearer. Moreover, it offers fresh methods for dealing with increasingly simplifying complex physical phenomena and advancing conceptual clarity.
VL  - 11
IS  - 4
ER  -

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Author Information

Teferi Mekit Dillo

Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia;Mineral Industry Development Institute, Ministry of Mine, Addis Ababa, Ethiopia

Contact Email

http://orcid.org/0009-0007-5964-6104

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APA Style

Dillo, T. M. (2025). Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion. International Journal of Theoretical and Applied Mathematics, 11(4), 65-70. https://doi.org/10.11648/j.ijtam.20251104.12

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ACS Style

Dillo, T. M. Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion. Int. J. Theor. Appl. Math. 2025, 11(4), 65-70. doi: 10.11648/j.ijtam.20251104.12

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AMA Style

Dillo TM. Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion. Int J Theor Appl Math. 2025;11(4):65-70. doi: 10.11648/j.ijtam.20251104.12

Copy | Download

@article{10.11648/j.ijtam.20251104.12,
  author = {Teferi Mekit Dillo},
  title = {Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {11},
  number = {4},
  pages = {65-70},
  doi = {10.11648/j.ijtam.20251104.12},
  url = {https://doi.org/10.11648/j.ijtam.20251104.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20251104.12},
  abstract = {The study introduces the arithmetical framework to derive classical kinematic equations without using calculus and provides comparable equations for displacement. The proposed method establishes a direct correspondence between kinematic quantities—velocity, acceleration, displacement, and time—and the elements of arithmetic progressions. Conventional calculus-based methods encounter constraints when applied to systems that suffer from accuracy; thus, it indicates that there are alternate mathematical tools and methodologies. A carefully chosen arithmetic-based model is developed, treating time as continuous when studied as a sequence and as discrete when regarded in a series. Further, acceleration is modeled as a deterministic continuous quantity, while velocity and displacement follow deterministic discrete patterns. Through transforming physical correlations directly to arithmetic patterns, this framework provides alternative distance equations. Based on standard summation, a comparative analysis of a constant-acceleration problem shows that the arithmetic model predicts displacement (47 m) with about 9% more accuracy than the classical calculus result (43 m). This confirms that the method is physically valid, and it not only makes calculations easier and reduces mistakes, but it also helps people understand motion under uniform acceleration better and gives more accurate results than the calculus-based model. The results imply that the arithmetic framework offers a unified way to connect discrete and continuous motion and gives classical mechanics a new mathematical base that makes calculations clearer. Moreover, it offers fresh methods for dealing with increasingly simplifying complex physical phenomena and advancing conceptual clarity.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Richness of Arithmetical Structure to Deliver Alternative Equations of Distance in Uniform Acceleration Motion
AU  - Teferi Mekit Dillo
Y1  - 2025/12/09
PY  - 2025
N1  - https://doi.org/10.11648/j.ijtam.20251104.12
DO  - 10.11648/j.ijtam.20251104.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 65
EP  - 70
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20251104.12
AB  - The study introduces the arithmetical framework to derive classical kinematic equations without using calculus and provides comparable equations for displacement. The proposed method establishes a direct correspondence between kinematic quantities—velocity, acceleration, displacement, and time—and the elements of arithmetic progressions. Conventional calculus-based methods encounter constraints when applied to systems that suffer from accuracy; thus, it indicates that there are alternate mathematical tools and methodologies. A carefully chosen arithmetic-based model is developed, treating time as continuous when studied as a sequence and as discrete when regarded in a series. Further, acceleration is modeled as a deterministic continuous quantity, while velocity and displacement follow deterministic discrete patterns. Through transforming physical correlations directly to arithmetic patterns, this framework provides alternative distance equations. Based on standard summation, a comparative analysis of a constant-acceleration problem shows that the arithmetic model predicts displacement (47 m) with about 9% more accuracy than the classical calculus result (43 m). This confirms that the method is physically valid, and it not only makes calculations easier and reduces mistakes, but it also helps people understand motion under uniform acceleration better and gives more accurate results than the calculus-based model. The results imply that the arithmetic framework offers a unified way to connect discrete and continuous motion and gives classical mechanics a new mathematical base that makes calculations clearer. Moreover, it offers fresh methods for dealing with increasingly simplifying complex physical phenomena and advancing conceptual clarity.
VL  - 11
IS  - 4
ER  -

Copy | Download