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Velocity from Potential Energy Formula
The calculator assumes that the given potential energy is fully converted into kinetic energy, with no losses from friction, air resistance, heat, or sound. It uses the kinetic energy relationship:
E = \frac{1}{2}mv^2To solve for velocity, the formula is rearranged as:
v = \sqrt{\frac{2E}{m}}To solve for mass, the formula is:
m = \frac{2E}{v^2}To solve for energy, the formula is:
E = \frac{1}{2}mv^2- E = total potential energy converted to kinetic energy
- m = mass of the object
- v = velocity of the object
The calculator converts your selected units to base SI units before solving: joules for energy, kilograms for mass, and meters per second for velocity. After the calculation, it converts the result back into the unit you selected.
If you enter energy and mass, it calculates velocity. If you enter mass and velocity, it calculates energy. If you enter energy and velocity, it calculates mass.
Common Unit Conversions
| Quantity | Unit | Base Unit Conversion |
|---|---|---|
| Energy | 1 kJ | 1,000 J |
| Energy | 1 ft·lbf | 1.35582 J |
| Mass | 1 lb | 0.453592 kg |
| Velocity | 1 mph | 0.44704 m/s |
| Velocity | 1 ft/s | 0.3048 m/s |
Velocity Results for Selected Energy and Mass Values
| Energy | Mass | Velocity |
|---|---|---|
| 100 J | 2 kg | 10 m/s |
| 500 J | 10 kg | 10 m/s |
| 1,000 J | 5 kg | 20 m/s |
| 2,000 J | 4 kg | 31.6228 m/s |
Example Calculations
Example 1: Find velocity from potential energy and mass
You have 1,000 J of potential energy and a mass of 5 kg.
v = \sqrt{\frac{2(1000)}{5}}v = \sqrt{400} = 20\text{ m/s}The velocity is 20 m/s.
Example 2: Find energy from mass and velocity
You have a 10 kg object moving at 12 m/s.
E = \frac{1}{2}(10)(12^2)E = 720\text{ J}The energy is 720 J.
FAQ
Is this the same as gravitational potential energy?
Not exactly. Gravitational potential energy is usually found with PE = mgh. This calculator starts with a known amount of potential energy and finds the velocity after that energy becomes kinetic energy. If you know height instead of energy, you would first calculate potential energy using mgh, then use that energy here.
Why does the formula use kinetic energy?
Velocity is tied directly to kinetic energy. When potential energy is converted into motion, the kinetic energy is equal to the usable converted potential energy. Under ideal conditions, that gives E = 1/2mv².
Can velocity be zero?
Velocity can be zero only when the kinetic energy is zero. If you are solving for mass, velocity cannot be zero because the formula divides by v². A zero velocity would make the mass calculation undefined.
