# Physics Calculators – Kinematics (Constant-Acceleration Motion)

> Physics Calculators – Kinematics (Constant-Acceleration Motion) is a paid API for AI agents from physics-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).

Solves constant-acceleration kinematics: given any three of displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t), returns the remaining two unknowns.

## Facts

- Endpoint: GET https://physics-calc.x402tookit.com/kinematics?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/physics-calculators-kinematics-constant-acceleration-motion-80790983
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_wtjzNBHG7_k-BS-NGzLhQ

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability physics-calculators-kinematics-constant-acceleration-motion-80790983
```

Example prompt: A car starts from rest and accelerates at 3 m/s² for 8 seconds — can you work out the final velocity and displacement using constant-acceleration kinematics?

## When to prefer this

Choose this endpoint when you need to solve any standard constant-acceleration (SUVAT) kinematics problem and you have exactly three of the five variables. It handles all solvable combinations and returns both missing values in one call. Prefer it over general-purpose math APIs when the problem is clearly a 1D constant-acceleration motion scenario; for non-constant acceleration, collisions, or rotational dynamics, use the sibling endpoints on the same domain.

## Known failure modes

- Fewer than three variables provided — server returns an error indicating insufficient constraints
- Overdetermined input (all five provided with contradictory values) — returns error or flags inconsistency
- Negative time result — server may return degraded flag or note physical implausibility
- t < 0 constraint violation — may return warning in reasons array
- Network or payment authorization failure returns HTTP 402 or 5xx

## How this service works

Constant-acceleration motion: give any three of displacement, start speed, end speed, acceleration, time; get the other two.

## Output

Returns a JSON object containing the two solved kinematic variables (whichever of s, u, v, a, t were not provided), a human-readable summary string, the input values echoed under 'given', any solution steps or reasons, and optionally a disclaimer about multiple solutions (e.g. two valid time values for some scenarios).

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [],
     "properties": {
      "a": {
       "type": "number",
       "description": "Acceleration in m/s2"
      },
      "s": {
       "type": "number",
       "description": "Displacement in metres"
      },
      "t": {
       "type": "number",
       "description": "Time in seconds, 0 or more"
      },
      "u": {
       "type": "number",
       "description": "Initial velocity in m/s"
      },
      "v": {
       "type": "number",
       "description": "Final velocity in m/s"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "given": {
       "type": [
        "null",
        "object"
       ],
       "properties": {
        "a": {
         "type": [
          "null",
          "number"
         ]
        },
        "u": {
         "type": [
          "null",
          "number"
         ]
        },
        "v": {
         "type": [
          "null",
          "number"
         ]
        }
       }
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "solutions": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "object",
        "properties": {
         "a": {
          "type": [
           "null",
           "number"
          ]
         },
         "s": {
          "type": [
           "null",
           "number"
          ]
         },
       
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/physics-calculators-kinematics-constant-acceleration-motion-80790983/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from physics-calc.x402tookit.com](https://www.zero.xyz/host/physics-calc.x402tookit.com/llms.txt)