Which of the following decreases in motion along a straight line with constant retardation while the body is moving away from the origin?

Options

A. Speed
B. Acceleration
C. Displacement
D. None of these

Explanation

To solve the question, we need to analyze the motion of a body moving along a straight line with constant retardation (negative acceleration) while it is moving away from the origin. We will evaluate which of the given options decreases during this motion.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- The body is moving in a straight line away from the origin with constant retardation.
- Retardation means that the body is experiencing negative acceleration.

2. **Defining Variables**:
- Let the initial velocity of the body be \( u \).
- The acceleration (retardation) is denoted as \( a \) (where \( a \) is a positive value, but since it's retardation, we consider it as negative in equations).

3. **Using the Equation of Motion**:
- We can use the equation of motion:
\[ V^2 = U^2 + 2aS \]
- Here, \( V \) is the final velocity, \( U \) is the initial velocity, \( a \) is the acceleration (which is negative), and \( S \) is the displacement.

4. **Analyzing the Displacement**:
- As the body moves away from the origin, the displacement \( S \) increases (i.e., \( S \) is positive).
- Since \( a \) is negative (retardation), we can rewrite the equation as:
\[ V^2 = U^2 - 2aS \]
- As \( S \) increases, the term \( -2aS \) becomes more negative (since \( -2a \) is a positive value), which means \( V^2 \) decreases.

5. **Conclusion on Speed**:
- Since \( V^2 \) decreases as \( S \) increases, it follows that \( V \) (the speed) must also decrease.
- Therefore, the speed of the body decreases as it moves away from the origin.

6. **Evaluating Other Options**:
- **Acceleration**: The acceleration remains constant (as given in the problem), so it does not decrease.
- **Displacement**: The displacement \( S \) increases as the body moves away from the origin, so it does not decrease.
- **None of These**: Since we have found that speed decreases, this option is incorrect.

### Final Answer:
The correct answer is that **speed decreases** as the body moves away from the origin.