If a particle is moving along straight line with increasing speed, then

Options

A. Its acceleration is negative
B. Its acceleration may be decreașing
C. Its acceleration is positive
D. Both (2) & (3)

Answer

To solve the question, "If a particle is moving along a straight line with increasing speed, then," we need to analyze the implications of the particle's motion.

### Step-by-Step Solution:

1. **Understanding Speed and Velocity**:
- Speed is the magnitude of velocity. When we say a particle is moving with increasing speed, it implies that its velocity is also increasing in magnitude.
- Since the motion is along a straight line, we can treat speed and velocity as equivalent in this context.

**Hint**: Remember that speed is a scalar quantity, while velocity is a vector quantity that includes direction.

2. **Defining Acceleration**:
- Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, it is given by:
\[ a = \frac{dv}{dt} \]
- Here, \(a\) is acceleration, \(dv\) is the change in velocity, and \(dt\) is the change in time.

**Hint**: Acceleration tells us how quickly velocity changes. A positive acceleration indicates an increase in velocity.

3. **Analyzing Increasing Speed**:
- If the speed (and thus the velocity) of the particle is increasing, it indicates that the acceleration must be positive. This is because a positive acceleration results in an increase in velocity over time.

**Hint**: Recall that if acceleration is negative, the velocity would decrease, contradicting the condition of increasing speed.

4. **Considering the Nature of Acceleration**:
- The question also mentions that the speed is increasing, which means that while the acceleration is positive, it could either be constant or decreasing. Thus, it is possible for the acceleration to be positive but not necessarily constant.

**Hint**: A decreasing acceleration can still be positive; it just means that the rate of increase in velocity is slowing down.

5. **Evaluating the Options**:
- Option 1: Acceleration is negative. (Incorrect, as we established that acceleration must be positive for speed to increase.)
- Option 2: Acceleration may be decreasing. (Correct, as acceleration can be positive and still decrease.)
- Option 3: Acceleration is positive. (Correct, since the speed is increasing.)
- Option 4: Both 2 and 3. (Correct, as both statements are true.)

6. **Conclusion**:
- The correct answer is option 4, which states that both 2 and 3 are correct.

### Final Answer:
The correct answer is **Option 4: Both 2 and 3**.

---