If something continues to increase its speed over time without any limit, it will eventually approach or even exceed the speed of light. According to our current understanding of physics, this has significant implications.
In the theory of special relativity, as an object approaches the speed of light, its relativistic mass increases, time dilation occurs, and its length contracts along its direction of motion. As the object gets closer to the speed of light, the energy required to further accelerate it also increases significantly.
When an object with mass reaches the speed of light, it would require an infinite amount of energy to accelerate it further, which is considered impossible within our current understanding of physics. Therefore, objects with mass, such as particles or macroscopic objects, cannot attain or exceed the speed of light.
However, it's important to note that this limitation does not apply to space itself. The expansion of the universe, as described by the theory of general relativity, can cause galaxies and other distant objects to move away from us at speeds greater than the speed of light. This is because the expansion of space itself is not constrained by the speed of light limitation.
In summary, if something were to continuously increase its speed without limit, it would eventually approach the speed of light but could not exceed it due to the fundamental principles of relativity.