For a moving body at any instant of time

Options

A. If the body is not moving, the acceleration is necessarily zero.
B. If the body is slowing, the retardation is negative
C. If the body is slowing, the distance is negative.
D. If displacement, velocity and acceleration at that instant are known, we can find the displacement at any given time in future.

Answer

To solve the question regarding the statements about a moving body at any instant of time, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement Analysis**:
- We have four statements to evaluate regarding a moving body.

2. **Statement 1**: "If the body is not moving, the acceleration is necessarily zero."
- **Evaluation**: This statement is **false**. A body can have zero velocity (not moving) but still have a non-zero acceleration. For example, when a ball is thrown upwards, at its maximum height, its velocity is zero, but it experiences gravitational acceleration downwards.

3. **Statement 2**: "If the body is slowing, the acceleration is negative."
- **Evaluation**: This statement is **false**. If a body is slowing down, it means that the acceleration is in the opposite direction to the velocity. If we consider the motion in the positive direction, the acceleration would be negative. However, it is important to note that the term "slowing" typically refers to a decrease in speed, which indicates that the acceleration is indeed negative.

4. **Statement 3**: "If the body is slowing, the distance is negative."
- **Evaluation**: This statement is **false**. Distance is a scalar quantity and cannot be negative. It only measures how much ground an object has covered regardless of its direction.

5. **Statement 4**: "If displacement, velocity, and acceleration at that instant are known, we can find the displacement at any given time in the future."
- **Evaluation**: This statement is **true**. Using kinematic equations, if we know the initial displacement (x0), initial velocity (u), and acceleration (a) at a given time, we can calculate the displacement (x) at any future time (t) using the equation:
\[ x = x_0 + ut + \frac{1}{2}at^2 \]

6. **Conclusion**:
- The only correct statement among the four is the last one. Therefore, the answer to the question is that the fourth statement is true.

### Summary of Findings:
- Statement 1: False
- Statement 2: False
- Statement 3: False
- Statement 4: True