According to our current understanding of physics, it is not possible for objects with mass to travel at or faster than the speed of light in a vacuum. This limitation is described by Einstein's theory of relativity.
One of the consequences of traveling at or near the speed of light is time dilation. As an object's speed approaches the speed of light, time slows down for that object relative to a stationary observer. However, even if an object were able to reach the speed of light, time would effectively stop for that object.
Considering the concept of traveling faster than light, it enters the realm of speculative physics. There are various theoretical concepts, such as wormholes or warp drives, that have been explored in science fiction and some theoretical frameworks like general relativity, but they are purely hypothetical at this point and not supported by empirical evidence.
If we assume faster-than-light travel were possible, it would introduce numerous paradoxes and contradictions, including the ability to violate causality by going back in time. These contradictions are part of the reason why faster-than-light travel is currently considered implausible based on our current understanding of the laws of physics.
In summary, according to our current knowledge, traveling at or faster than the speed of light is not possible for objects with mass, and it is unclear what would happen if such speeds were achievable.