Accelerating an object with mass to the speed of light is not possible according to our current understanding of physics. As an object with mass approaches the speed of light, its energy and momentum increase significantly, and the amount of energy required to further accelerate it also increases. As the object approaches the speed of light, its mass effectively becomes infinite, making it impossible to reach or exceed the speed of light.
However, if we assume a hypothetical scenario where an object with mass could be accelerated arbitrarily close to the speed of light, we can still estimate the time it would take to reach a high fraction of the speed of light using an idealized model.
Let's consider a mass driver, which is a device designed to accelerate objects using electromagnetic forces. One common approximation is to use constant acceleration throughout the entire process, although in reality, the acceleration would not be constant due to factors like energy constraints, relativistic effects, and the need to limit forces on the accelerated object.
In this idealized scenario, we can use the equations of motion from classical physics. The equation to calculate the time required to accelerate from rest to a given velocity with constant acceleration is:
t = v / a
Where: t is the time, v is the final velocity, and a is the constant acceleration.
Assuming we want to calculate the time to reach a fraction of the speed of light, let's say 90% (0.9c), we can substitute the speed of light (c) with 0.9c in the equation.
t = (0.9c) / a
Please note that this is a simplified model and does not account for relativistic effects, energy constraints, or the practical limitations of acceleration systems. Additionally, it assumes constant acceleration throughout the entire process, which may not be achievable in reality.
Given these limitations, the time required to accelerate to a high fraction of the speed of light would still be extremely large, even with hypothetical technologies.