A body whose speed in a particular direction is constant

Options

A. must be accelerating
B. must be retarding
C. has a constant velocity
D. all the above

Answer

To solve the question, "A body whose speed in a particular direction is constant," we need to analyze the implications of constant speed in a specific direction.

### Step-by-Step Solution:

1. **Understanding Speed and Direction**:
- Speed is defined as the magnitude of velocity, which is a vector quantity that includes both magnitude and direction. When we say that the speed is constant in a particular direction, it means that the body is moving with a fixed speed and is not changing its direction.

2. **Definition of Constant Velocity**:
- If the speed is constant in a particular direction, then the velocity is also constant. This is because velocity encompasses both speed and direction. Therefore, if both the speed and the direction are not changing, we can conclude that the velocity is constant.

3. **Acceleration**:
- Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, it is expressed as \( a = \frac{dv}{dt} \).
- Since we have established that the velocity is constant, the change in velocity (\( dv \)) is zero. Therefore, the acceleration (\( a \)) must also be zero.

4. **Evaluating the Options**:
- The question provides the following options:
- Must be accelerating
- Must be retarding
- Has a constant velocity
- All of the above
- Since we have determined that the body has a constant speed in a particular direction, it does not accelerate or retard. The only correct option is that it has a constant velocity.

5. **Conclusion**:
- The answer to the question is that the body has a constant velocity.

### Final Answer:
**C. Has a constant velocity**

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