In Einstein's equation, E = mc², the equation relates energy (E) to mass (m) and the speed of light (c). This equation describes the equivalence of energy and mass, and it is commonly associated with the theory of relativity.
When considering the velocity of an object whose mass increases with increasing velocity, we need to take into account the concept of relativistic mass. The relativistic mass (m') of an object is given by:
m' = m / √(1 - v²/c²)
Where: m' is the relativistic mass, m is the rest mass (mass at rest), v is the velocity of the object, and c is the speed of light in a vacuum.
To calculate the velocity of the object, we can rearrange the equation to solve for v:
v = √((1 - m²/m'²) * c²)
Note that the rest mass (m) remains constant, and the relativistic mass (m') increases with velocity. As the object approaches the speed of light, its relativistic mass increases, and the velocity approaches c.
It's important to mention that the concept of relativistic mass is not commonly used in modern physics. Instead, the relativistic energy and momentum equations are more commonly employed to describe the behavior of objects with varying velocities. These equations take into account the relationship between energy, momentum, and velocity while keeping the mass constant.