{
  "abstract": "The second equation of motion, s = ut + ½at², is usually derived by integrating velocity or from the area under a velocity-time graph. This paper presents an alternative, calculus-free derivation based on summing the displacement covered in successive unit-time intervals. Assuming constant acceleration and using the velocity at the start of each interval, the total displacement is found to be s = ut + ½at² − ½at. The extra term −½at is shown to be a discretisation error caused by ignoring the change of velocity within each interval. Generalising to a time step h gives s = ut + ½at² − ½ath, which reduces to the standard equation as h → 0. Using the mid-interval velocity removes the error exactly. The method gives students an elementary, summation-based explanation of where the factor ½ in ½at² comes from and links kinematics to the idea of Riemann sums.\n\nIndependent student research. This preprint has not been peer-reviewed. An AI assistant was used to check the algebra and help with writing.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Amritanshu Asthana",
      "orcid": "0009-0005-8445-5364"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19rraswyezq4f.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23657193",
  "fulltext_url": null,
  "id": "19rraswyezq4f",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23657193",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23657193/files/A%20Discrete-Time%20Summation%20Derivation%20of%20the%20Second%20Equation%20of%20Motion.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19rraswyezq4f.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:39Z",
      "native_id": "23657193",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23657193"
    }
  ],
  "subjects": [],
  "title": "A Discrete-Time Summation Derivation of the Second Equation of Motion",
  "title_text": "A Discrete-Time Summation Derivation of the Second Equation of Motion",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:39Z",
  "url": "https://research.draconitic.com/paper/19rraswyezq4f",
  "venue": "Zenodo",
  "versions": []
}