According to the theory of special relativity, it is not possible for an object with mass to reach or exceed the speed of light in a vacuum. The speed of light, denoted by 'c', is considered the ultimate speed limit in the universe. As an object with mass approaches the speed of light, its relativistic mass, energy, and momentum increase, making it more difficult to accelerate further.
However, let's consider a hypothetical scenario where we ignore this limitation and assume that a spaceship somehow reaches the speed of light. In this case, the effects of acceleration become significant and unusual.
Time Dilation: According to special relativity, as an object accelerates, time dilation occurs. Time appears to pass more slowly for the object in motion relative to a stationary observer. As the spaceship's acceleration increases, time dilation would become more pronounced. From the perspective of the spaceship, time for the rest of the universe would appear to speed up, while time within the spaceship would appear to pass normally.
Mass Increase: As the spaceship accelerates, its relativistic mass would increase. The relativistic mass is given by the equation m = m₀ / √(1 - v²/c²), where m₀ is the rest mass (mass at rest) of the spaceship, v is its velocity, and c is the speed of light. As the spaceship approaches the speed of light, its mass would increase towards infinity, requiring infinite energy to continue accelerating. This is one of the reasons why it is impossible for an object with mass to reach or exceed the speed of light.
Length Contraction: According to the principle of length contraction in special relativity, an object in motion appears shorter along its direction of motion as observed by a stationary observer. As the spaceship accelerates towards the speed of light, its length in the direction of motion would appear to contract from the perspective of an external observer.
It's important to note that these effects become more pronounced as the spaceship approaches the speed of light, but they do not apply at or beyond the speed of light. Special relativity describes the behavior of objects with mass up to the speed of light but not beyond it. The theory of general relativity becomes more relevant when considering the behavior of objects in the presence of strong gravitational fields or when attempting to study the nature of space-time near the speed of light.