According to Einstein's theory of relativity, as an object approaches the speed of light, its mass increases. This phenomenon is described by the relativistic mass equation:
m = m_0 / √(1 - (v^2 / c^2))
where: m is the relativistic mass, m_0 is the rest mass (mass at rest) of the object, v is the velocity of the object, and c is the speed of light in a vacuum.
As the object approaches the speed of light, v approaches c, and the denominator in the equation approaches zero. Consequently, the mass of the object increases significantly.
However, it is important to note that as an object approaches the speed of light, an infinite amount of force would be required to continue accelerating it. This is due to the relationship between force (F), mass (m), and acceleration (a), defined by Newton's second law of motion:
F = m * a
As the mass of the object approaches infinity, an infinite amount of force would be needed to produce any finite acceleration. Thus, it is not possible to accelerate an object with mass to the speed of light using realistic means.
It is worth mentioning that as an object with mass approaches the speed of light, its energy and momentum also increase. This is captured by Einstein's equation:
E = m * c^2
where E is the energy of the object.
In summary, the force required to accelerate an object with mass to the speed of light would be infinite, and its mass would approach infinity as it approaches the speed of light. However, reaching the speed of light is not possible for massive objects according to our current understanding of physics.