According to the theory of relativity, as the velocity of an object approaches the speed of light, the total energy of the object does increase. This is described by Einstein's famous equation, E=mc^2, where E represents the total energy of the object, m is its rest mass, and c is the speed of light in a vacuum.
In classical physics, the total energy of an object can be calculated using the formula:
E = (1/2)mv^2
where m is the mass of the object and v is its velocity. According to this equation, the total energy of an object increases with the square of its velocity.
However, in the theory of relativity, the equation E=mc^2 shows that even at rest (v=0), an object possesses an energy equivalent to its rest mass multiplied by the square of the speed of light. As the velocity of the object increases, its kinetic energy contributes to the total energy, and the overall energy of the object increases. As the velocity approaches the speed of light, the kinetic energy dominates, and the total energy becomes significantly larger.
It's important to note that the increase in total energy is not proportional to the velocity itself, but rather to the relativistic mass of the object, which takes into account the effects of velocity on mass. This is one of the fundamental aspects of the theory of relativity that differs from classical Newtonian physics.