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 analyze the motion of a body at any instant of time, we need to consider the concepts of velocity, acceleration, and force. Let's break down the question step by step.

### Step 1: Understand the Definitions
- **Velocity**: The speed of an object in a given direction.
- **Acceleration**: The rate of change of velocity with respect to time.
- **Force**: According to Newton's second law, force is the product of mass and acceleration (F = ma).

### Step 2: Analyze the Case When the Body is Not Moving
- If a body is not moving, its velocity is zero (v = 0).
- The acceleration of the body can also be zero (a = 0) if it is at rest and not changing its state of motion.

### Step 3: Determine the Implications for Force
- If the body is at rest and not accelerating (a = 0), then according to Newton's second law (F = ma), the force acting on the body must also be zero (F = 0).
- However, it is important to note that a body can be at rest while experiencing forces. For example, if two equal and opposite forces act on the body, the net force is zero, and the body remains at rest.

### Step 4: Analyze the Case When the Body is Moving
- If a body is moving, it has a non-zero velocity (v ≠ 0).
- The acceleration can be zero (constant velocity) or non-zero (changing velocity).
- If the body is moving with constant velocity (a = 0), then the net force acting on it is also zero (F = 0), meaning that all forces are balanced.
- If the body is accelerating (a ≠ 0), then there must be a net force acting on it (F ≠ 0).

### Conclusion
- If the body is not moving, it is necessary that the net force is zero, but not all forces acting on it must be zero.
- If the body is moving, it is not necessary that the force is zero; it can be zero if the body moves with constant velocity, or it can be non-zero if the body is accelerating.

### Summary
1. If a body is not moving, its acceleration is zero, and the net force is zero.
2. If a body is moving, it can have zero net force (constant velocity) or non-zero net force (accelerating).