According to our current understanding of physics, objects with mass cannot reach or exceed the speed of light. As an object with mass approaches the speed of light, its energy and momentum increase dramatically, requiring an infinite amount of energy to reach the speed of light.
However, if we consider a hypothetical scenario where an object with massless particles, such as a photon, is already traveling at the speed of light, and we want to increase its speed by half again, we can explore the concept.
In this case, the equation we can use to calculate the energy required is the relativistic energy-momentum relationship:
E = (γ - 1)mc²
where: E is the energy of the object, γ (gamma) is the Lorentz factor, given by γ = 1/√(1 - v²/c²) with v being the velocity and c being the speed of light, m is the mass of the object, and c is the speed of light.
Since we want to increase the speed by half again, we need to calculate the new velocity and then calculate the corresponding energy. Let's assume the initial velocity is c (speed of light), and we want to increase it by half, resulting in a new velocity of (3/2)c.
Plugging these values into the equation, we have:
E = (γ - 1)mc² E = (1/√(1 - (3/2)²c²) - 1)mc²
Simplifying the equation and substituting c² as (299,792,458 m/s)², we can calculate the energy required. However, it's important to note that in the context of known physics, this scenario of objects with massless particles like photons being accelerated is not applicable due to the fundamental restrictions imposed by special relativity.