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.

Answer

To solve the problem step by step, we can follow this reasoning:

### Step 1: Understand the nature of the force
The problem states that a particle is acted upon by a force of constant magnitude that is always perpendicular to the velocity of the particle. This means that the force does not do work on the particle since work done is given by the dot product of force and displacement.

**Hint:** Remember that when force is perpendicular to the direction of motion, it does not change the speed of the particle.

### Step 2: Analyze the work done by the force
Since the force is perpendicular to the velocity, we can express this mathematically as:
\[ \mathbf{F} \cdot \mathbf{v} = 0 \]
This implies that the work done \( W \) by the force over any displacement is zero:
\[ W = \mathbf{F} \cdot \mathbf{d} = 0 \]

**Hint:** Recall that work done is related to the change in kinetic energy.

### Step 3: 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:
\[ W = \Delta KE = KE_{final} - KE_{initial} \]
Since we established that the work done is zero, we have:
\[ KE_{final} - KE_{initial} = 0 \]
This implies:
\[ KE_{final} = KE_{initial} \]

**Hint:** Think about what it means for kinetic energy to remain constant.

### Step 4: Conclude about the kinetic energy
Since the kinetic energy is constant, we can conclude that the speed of the particle does not change. However, the direction of the velocity can change due to the perpendicular force, leading to circular or curved motion.

**Hint:** Consider the implications of constant speed in terms of motion.

### Step 5: Final conclusion
Thus, we conclude that the kinetic energy of the particle remains constant throughout its motion. Therefore, the correct answer to the question is that the kinetic energy is constant.

**Final Answer:** The kinetic energy is constant.