Yes, according to the theory of relativity, as the velocity of an object increases, its total energy does increase. This concept is described by the equation for the total energy of an object, which includes both its kinetic energy and its rest energy (the energy it possesses at rest).
In special relativity, the total energy of an object is given by the equation:
E = mc^2 / √(1 - v^2/c^2)
Where: E is the total energy of the object, m is its rest mass, c is the speed of light in a vacuum, v is the velocity of the object.
As the object's velocity (v) approaches the speed of light (c), the denominator of the equation approaches zero, causing the total energy (E) to increase. This means that an object's energy becomes increasingly large as it approaches the speed of light.
It's worth noting that the increase in energy comes from the object's kinetic energy, not its rest mass. The object's mass itself, as observed by an external observer, remains constant regardless of its velocity. However, the total energy, which includes both the rest energy and the energy associated with motion, increases as the velocity increases.