A particle is acted upon by a force of constant magnitude which is always perpendicular 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 moves in a straight line

Explanation

To solve the problem, we need to analyze the motion of a particle acted upon by a constant magnitude force that is always perpendicular to its velocity. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Forces Acting on the Particle
- The particle is subjected to a force of constant magnitude that is always perpendicular to its velocity.
- Since the force is perpendicular to the velocity, it does not do any work on the particle. This means that the kinetic energy of the particle remains constant.

**Hint:** Remember that work done by a force is given by the dot product of force and displacement. If the force is perpendicular to the displacement, the work done is zero.

### Step 2: Analyze the Motion
- The direction of the velocity vector changes due to the perpendicular force, which means that the particle is undergoing a change in direction.
- Since the force is constant in magnitude and always perpendicular to the velocity, this indicates that the particle is moving in a circular path.

**Hint:** Consider how the direction of the velocity vector changes when a force acts perpendicular to it. This is characteristic of circular motion.

### Step 3: Determine the Nature of Velocity and Acceleration
- Velocity is a vector quantity that has both magnitude and direction. Although the magnitude of the velocity (speed) remains constant, the direction changes continuously.
- Acceleration is also a vector quantity, and since it is directed towards the center of the circular path (due to the perpendicular force), its direction is also changing.

**Hint:** Recall that for a vector quantity to be constant, both its magnitude and direction must remain unchanged.

### Step 4: Evaluate Kinetic Energy
- The kinetic energy (KE) of the particle is given by the formula \( KE = \frac{1}{2}mv^2 \).
- Since the speed (magnitude of velocity) is constant, the kinetic energy remains constant as well.

**Hint:** Kinetic energy depends only on the speed of the particle, not its direction.

### Step 5: Conclusion
- From the analysis, we conclude that:
- The velocity is not constant because its direction is changing.
- The acceleration is not constant because its direction is also changing.
- The kinetic energy is constant due to constant speed.
- The particle does not move in a straight line; it moves in a circular path.

Thus, the correct answer is that the kinetic energy of the particle remains constant.

**Final Answer:** The kinetic energy of the particle is constant.