Under the action of a constant force, A particle is experiencing a constant acceleration. The power is

Options

A. Positive constant
B. Negative constant
C. Increasing uniformly with time
D. Decreasing uniformly with time

Answer

To solve the problem, we need to analyze the relationship between force, acceleration, velocity, and power.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- A particle is under the action of a constant force.
- This constant force results in a constant acceleration.

2. **Recall the Relationship Between Force and Acceleration**:
- According to Newton's second law, \( F = ma \), where \( F \) is the force, \( m \) is the mass of the particle, and \( a \) is the acceleration.
- Since the force is constant, the acceleration \( a \) is also constant.

3. **Determine the Velocity**:
- The velocity of the particle changes over time due to the constant acceleration.
- The relationship is given by:
\[ v = u + at \]
where \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is the constant acceleration, and \( t \) is the time.

4. **Calculate Power**:
- Power (\( P \)) is defined as the rate of doing work or the rate of energy transfer. It can also be expressed as:
\[ P = F \cdot v \]
- Since the force \( F \) is constant and the velocity \( v \) is increasing with time (because of constant acceleration), we can express power as:
\[ P = F \cdot (u + at) \]
- As time \( t \) increases, the velocity \( v \) increases, leading to an increase in power.

5. **Conclusion**:
- Since the power is directly proportional to the increasing velocity (which is a function of time), we conclude that the power increases uniformly with time.

### Final Answer:
The power is increasing uniformly with time.