Final answer:
The mass of a particle does not decrease with increasing acceleration in the context of special relativity. Instead, the particle's relativistic mass increases, and the rest mass remains constant.
Step-by-step explanation:
In the context of special relativity, the statement that the mass of a particle decreases with increasing acceleration is incorrect. According to Einstein's theory, as the velocity of a particle approaches the speed of light, its mass effectively increases due to the increase in relativistic mass. This is because the relativistic mass is dependent on velocity and is given by the equation m = m0 / sqrt(1 - v^2/c^2), where m0 is the rest mass, v is the velocity, and c is the speed of light. The rest mass, m0, remains constant, but as v increases, the denominator becomes smaller, resulting in a larger relativistic mass.
The force F applied to a particle is indeed equal to the particle's mass multiplied by its acceleration (F = ma). However, in special relativity, it is crucial to distinguish between rest mass and relativistic mass. When the particle is accelerated, the relativistic mass increases, which means the particle experiences less acceleration for the same force. Hence, acceleration is inversely proportional to mass, and not the rate at which mass changes. The rest mass of the particle remains constant regardless of the acceleration.