{
  "schemaVersion": 1,
  "slug": "kinematic-velocity-calculator",
  "category": "science",
  "kind": "implementation",
  "independentValidation": false,
  "implementationHash": "05a2d2ad0c276d3803cfe37a561c6960bb4cce94320d63f875a8559c7508cfc5",
  "provenance": "Generated from the calculation contract used by the published page. Publication is not external validation.",
  "sourceFiles": [
    "data/calculators/kinematic-velocity-calculator.json",
    "src/engine.js"
  ],
  "runtimeSource": "/sources/engine.txt",
  "runtimeHash": "5c888d8898afbdee36267bb9977829e1e2ac568f6677c8ee87469c139864645c",
  "scope": "The compute function records implemented equations, constants, lookup tables and custom rules. Inputs record defaults and allowed values; outputs record precision and units. Defaults are examples, not recommendations. General background references are not evidence for this specific algorithm.",
  "publishedFormula": {
    "formula": "v = u + a × t; d = u × t + ½ × a × t²; t_stop = −u ÷ a when u × a < 0",
    "vars": [
      [
        "v",
        "Final velocity (m/s)"
      ],
      [
        "u",
        "Initial velocity (m/s)"
      ],
      [
        "a",
        "Constant acceleration (m/s²)"
      ],
      [
        "t",
        "Elapsed time (s)"
      ],
      [
        "d",
        "Displacement (m)"
      ]
    ],
    "note": "Average velocity = d ÷ t. Time to rest is shown only when acceleration opposes the initial velocity; km/h = m/s × 3.6."
  },
  "externalEvidence": {
    "reviewedAt": "2026-10-04",
    "sources": [
      {
        "name": "OpenStax — Motion with constant acceleration",
        "url": "https://openstax.org/books/university-physics-volume-1/pages/3-4-motion-with-constant-acceleration"
      }
    ],
    "basis": "Final velocity is initial velocity + acceleration × time; displacement is initial velocity × time + acceleration × time² / 2.",
    "limitations": "Assumes constant signed acceleration in one dimension. Time to stop applies only when velocity and acceleration oppose; the displayed zero otherwise is a sentinel, not a prediction of immediate stopping.",
    "implementationHash": "05a2d2ad0c276d3803cfe37a561c6960bb4cce94320d63f875a8559c7508cfc5"
  },
  "contract": {
    "compute": "const v = initialVelocity + acceleration*time; const d = initialVelocity*time + 0.5*acceleration*time*time; const avg = time > 0 ? d/time : initialVelocity; return { finalVelocity: v, displacement: d, averageVelocity: avg, finalVelocityKph: v*3.6, distanceKm: d/1000, timeToStop: initialVelocity*acceleration<0 ? -initialVelocity/acceleration : 0 };",
    "inputs": [
      {
        "name": "initialVelocity",
        "type": "number",
        "default": 0,
        "min": -100000,
        "max": 100000,
        "step": 0.01
      },
      {
        "name": "acceleration",
        "type": "number",
        "default": 9.81,
        "min": -100000,
        "max": 100000,
        "step": 0.01
      },
      {
        "name": "time",
        "type": "number",
        "default": 3,
        "min": 0,
        "max": 1000000,
        "step": 0.01
      }
    ],
    "outputs": [
      {
        "name": "finalVelocity",
        "precision": 3,
        "unit": "m/s"
      },
      {
        "name": "displacement",
        "precision": 3,
        "unit": "m"
      },
      {
        "name": "averageVelocity",
        "precision": 3,
        "unit": "m/s"
      },
      {
        "name": "finalVelocityKph",
        "precision": 2,
        "unit": "km/h"
      },
      {
        "name": "distanceKm",
        "precision": 5,
        "unit": "km"
      },
      {
        "name": "timeToStop",
        "precision": 3,
        "unit": "s"
      }
    ],
    "interpret": null
  }
}