According to our current understanding of physics based on Einstein's theory of relativity, as an object with mass approaches the speed of light, its energy and momentum increase significantly. As a result, it requires an infinite amount of energy to accelerate an object with mass to the speed of light. This means that it's not possible for a rocket ship with mass to reach or exceed the speed of light, regardless of the constant rate of acceleration or the availability of fuel.
As an object with mass accelerates, its speed will continue to increase, but it will never reach the speed of light. The closer it gets to the speed of light, the more energy is required to further accelerate it. Additionally, as an object's speed increases, its mass also increases according to the theory of relativity, making it even more difficult to accelerate.
However, it's important to note that these principles apply to objects with mass. According to relativity, massless particles such as photons (particles of light) travel at the speed of light in a vacuum. So while a rocket with mass cannot reach the speed of light, massless particles always travel at that speed.