In Einstein's theory of special relativity, the equation E = mc² relates energy (E) and mass (m). This equation states that energy and mass are interchangeable, and the c² term represents the square of the speed of light, which is a fundamental constant.
As an object approaches speeds close to the speed of light (c), its mass does not simply increase linearly with velocity. Instead, the mass of the object increases according to the relativistic mass equation:
m = m₀ / √(1 - v²/c²)
Here, m is the relativistic mass of the object, m₀ is the object's rest mass (mass at rest), v is the velocity of the object, and c is the speed of light.
To calculate the velocity (v) of an object with a given mass (m), you would need to rearrange the above equation:
v = √(1 - (m₀/m)²) * c
In this equation, you know the object's rest mass (m₀) and its relativistic mass (m). By substituting these values into the equation, you can solve for the velocity (v) of the object.
It's important to note that as an object approaches the speed of light, its relativistic mass increases significantly, but its velocity can never actually reach or exceed the speed of light in a vacuum (c). The equation above becomes undefined when v equals c.