A particle is moving under the influence of a force which is fixed in magnitude and acting at an angle `theta` in the direction of motion. The path described by the particle is

Options

A. a circle
B. an ellipse
C. a parabola
D. a straight line

Explanation

To solve the problem, we need to analyze the motion of a particle under the influence of a force that is fixed in magnitude and acts at an angle \( \theta \) to the direction of motion.

### Step-by-Step Solution:

1. **Understanding the Force and Motion**:
The particle is moving in a certain direction with a velocity \( \vec{v} \). A force \( \vec{F} \) is applied at an angle \( \theta \) to the direction of this motion.

2. **Components of the Force**:
The force can be broken down into two components:
- A component along the direction of motion: \( F_{\parallel} = F \cos(\theta) \)
- A component perpendicular to the direction of motion: \( F_{\perpendicular} = F \sin(\theta) \)

3. **Effect of the Force**:
The component \( F_{\parallel} \) will cause the particle to accelerate in the direction of motion, while \( F_{\perpendicular} \) will change the direction of the velocity of the particle.

4. **Acceleration Calculation**:
According to Newton's second law, the acceleration \( \vec{a} \) of the particle can be calculated using:
\[ \vec{a} = \frac{\vec{F}}{m} \]
where \( m \) is the mass of the particle. The acceleration will have both a tangential component (due to \( F_{\parallel} \)) and a normal component (due to \( F_{\perpendicular} \)).

5. **Path of the Particle**:
The presence of a force at an angle \( \theta \) means that the particle will not move in a straight line. Instead, the combination of the tangential acceleration (which increases the speed) and the normal acceleration (which changes the direction) will result in a curved path.

6. **Identifying the Path Shape**:
The path described by the particle under these conditions is similar to that of a projectile motion, which is a parabolic trajectory. This is because the particle is subjected to a constant acceleration in the direction of the force while also changing direction.

7. **Conclusion**:
Therefore, the path described by the particle is a parabola.

### Final Answer:
The path described by the particle is a **parabola**.

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