Source: https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/

instrument / verified-clean

# Impulse-Momentum Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/impulse-momentum-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

**Tranche**: tranche-4

**Evidence ID**: t4-191

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The listed relationships are standard under constant-mass, one-dimensional assumptions, but the specification needs clarification of force variability, vector handling, required inputs for each output, and unit normalization before it can receive PASS.

### Formula and scope findings

- J=FΔt is correct only when F is constant or represents the average net force over the interval; the general formula is J=∫F(t)dt.

- The formula for velocity change from force-time inputs must explicitly include Δv=J/m=FΔt/m; without mass, F and Δt alone cannot determine Δv.

- Impulse and momentum change are vectors. A scalar implementation needs an explicit one-dimensional or componentwise sign convention.

- The relation mΔv assumes constant mass. Variable-mass systems require additional treatment.

### Unit assumptions

- Use net force, not an arbitrary single force, and use SI units: F in newtons, Δt in seconds, m in kilograms, Δv in meters per second, J in newton-seconds (equivalent to kg·m/s).

- F, Δv, and J are treated as signed scalar quantities along one chosen axis, or as corresponding vector components.

- The time interval Δt is a nonnegative duration.

- If alternative units are accepted, they must be converted consistently; for example, 1 kN=1000 N and 1 ms=0.001 s.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-mass input creates an undefined velocity-change result through division by zero. The sign convention is also underspecified: treating force as signed versus magnitude-only changes both impulse and velocity-change signs.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "F_N": 120,
    "delta_t_s": 0.25,
    "m_kg": 60
  },
  "expected_outputs": {
    "J_Ns": 30,
    "delta_v_m_per_s": 0.5
  },
  "working": "J=FΔt=120 N×0.25 s=30 N·s. Δv=J/m=30 kg·m/s÷60 kg=0.5 m/s."
}
````

## Related workflows

[Kinematics & Collisions TutorJ=Δp](<https://guthlabs.ai/docs/instrument-workflows/kinematics-tutor/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`