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Particle Speed from Kinetic Energy Calculator — result sheet
Solve the classical non-relativistic kinetic-energy equation for particle speed and momentum from energy and mass.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For classical translational motion, speed v = √(2K/m); momentum magnitude p = √(2mK).
This is the reverse direction of the familiar kinetic-energy relationship: given positive translational energy and mass, it solves for speed. Momentum is included as a consistency check. The classical model must not be used when the calculated speed is close to the speed of light; relativistic energy is a different model.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Translational kinetic energy — J; minimum 1.0E-6; maximum 1000000000000
- Particle mass — kg; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Translational kinetic energy | 450 |
| Particle mass | 0.08 |
A 0.08 kg particle with 450 J of translational kinetic energy has classical speed about 106.066 m/s (381.838 km/h) and momentum about 8.485 kg·m/s.
Assumptions and limits
- Energy is translational kinetic energy measured in joules and mass is in kilograms.
- The particle is modeled classically with v much smaller than the speed of light.
- The returned speed is a magnitude, so direction and sign are not represented.
- Rest energy, relativistic momentum, rotation, internal energy, and mass changes are not modeled.
- A very large energy-to-mass ratio can make the classical answer physically inappropriate even when the arithmetic is finite.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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