Step 1: Understanding the terms:

• Acceleration: The rate of change of velocity with respect to time.
• Retardation: A special case of acceleration where the speed of the body decreases, often denoted as negative acceleration.
• Displacement: The change in position of an object in a particular direction.

Step 2: Evaluating each option:

• Option A: If the body is not moving (that is, its speed is 0), the acceleration must also be 0. This holds true since an object at rest will not change its state of motion unless acted upon by an external force (Newton's First Law). Therefore, the acceleration is necessarily zero.
• Option B: If the body is slowing down, this indicates that the acceleration is in the opposite direction to the velocity, which can be described as retardation. However, retardation being 'negative' can be misleading; it is more accurate to say the acceleration is negative in the context of motion. Thus, this option is not precise.
• Option C: If the body is slowing down, the distance covered can still be positive. Distance is a scalar quantity and is always non-negative, regardless of the direction of motion. Therefore, this statement is incorrect.
• Option D: While knowing displacement, velocity, and acceleration at a given instant can allow us to predict future positions under certain conditions (using kinematic equations), it does not guarantee we can determine displacement at any given future time without making additional assumptions about uniformity of motion or acceleration.

Conclusion: Thus, the only valid statement is option A, which accurately describes the relationship between being at rest and acceleration. Therefore, the correct answer is A.