A particle is acted upon by a force of constant magnitude which is always perpendiculr to the velocity of the particle. The motion of the particle takes place in a plane. It follows that

Options

A. its velocity is constant
B. its acceleration is constant
C. its kinetic energy is constant
D. it move in a circular path

Answer

To solve the problem step by step, we will analyze the situation where a particle is acted upon by a force of constant magnitude that is always perpendicular to its velocity.

### Step 1: Understand the Given Information
We have a particle that is subjected to a constant force. The key points are:
- The force has a constant magnitude.
- The force is always perpendicular to the velocity of the particle.
- The motion occurs in a plane.

### Step 2: Analyze the Force and Velocity Relationship
Since the force is always perpendicular to the velocity, we can conclude that:
- The direction of the force does not do any work on the particle because work is defined as \( W = F \cdot S = F S \cos \theta \), where \( \theta \) is the angle between the force and displacement vectors.

### Step 3: Calculate the Work Done
Since the force is perpendicular to the velocity, the angle \( \theta \) is 90 degrees. Thus, we have:
\[ W = F S \cos(90^\circ) = F S \cdot 0 = 0 \]
This means that the work done by the force on the particle is zero.

### Step 4: Apply the Work-Energy Theorem
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy:
\[ W = K_{\text{final}} - K_{\text{initial}} \]
Since we found that \( W = 0 \), we can write:
\[ 0 = K_{\text{final}} - K_{\text{initial}} \]
This implies:
\[ K_{\text{final}} = K_{\text{initial}} \]
Thus, the kinetic energy of the particle remains constant.

### Step 5: Conclusion
Since the kinetic energy of the particle does not change, we conclude that the kinetic energy of the particle remains constant throughout its motion.

### Final Answer
The kinetic energy of the particle is constant.

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