To solve the question, "If a constant force acts on a particle, its acceleration will," we can follow these steps:
### Step 1: Understand the relationship between force, mass, and acceleration
According to Newton's second law of motion, the relationship between force (F), mass (m), and acceleration (a) is given by the equation:
\[ F = m \cdot a \]
This means that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
### Step 2: Analyze the given conditions
The problem states that a constant force is acting on the particle. This implies that the value of F is constant. Additionally, we need to consider the mass of the particle. If the velocity of the particle is much less than the speed of light (non-relativistic speeds), the mass of the particle can be considered constant.
### Step 3: Determine the effect of constant force on acceleration
Since both the force (F) and mass (m) are constant (under non-relativistic conditions), we can rearrange the equation to find acceleration:
\[ a = \frac{F}{m} \]
Since F is constant and m is constant, it follows that the acceleration (a) will also remain constant.
### Step 4: Consider relativistic effects
However, if the velocity of the particle increases and approaches a significant fraction of the speed of light, relativistic effects must be considered. In relativity, the mass of the particle increases with velocity according to the equation:
\[ m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} \]
where \( m_0 \) is the rest mass, \( v \) is the velocity of the particle, and \( c \) is the speed of light.
### Step 5: Analyze the implications of increasing velocity
As the velocity \( v \) approaches the speed of light \( c \), the denominator in the mass equation decreases, causing the mass \( m \) to increase. Since the force \( F \) remains constant, but the mass \( m \) is increasing, the acceleration \( a \) must decrease:
\[ a = \frac{F}{m} \]
As \( m \) increases, \( a \) decreases.
### Conclusion
Initially, if the particle's velocity is much less than the speed of light, the acceleration remains constant. However, as the velocity increases and becomes comparable to the speed of light, the acceleration decreases. Therefore, the correct answer to the question is that the acceleration will gradually decrease.
### Final Answer
The acceleration will gradually decrease.
