Under what conditons (s) will an object be in equilibrium ?

Options

A. Only if it at rest
B. Only if moving with constant velocity
C. Only if it is moving with constant acceleration
D. If it is either at rest or moving with constant velocity

Answer

To determine the conditions under which an object is in equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Equilibrium**: An object is said to be in equilibrium when the net force acting on it is zero. This means that all the forces acting on the object balance each other out.

2. **Applying Newton's Second Law**: According to Newton's second law, force (F) is equal to mass (m) times acceleration (a), expressed as:
\[ F = m \cdot a \]
For an object to be in equilibrium, the net force must be zero, which implies:
\[ F_{\text{net}} = 0 \]

3. **Setting Up the Equation**: If the net force is zero, we can set up the equation:
\[ m \cdot a = 0 \]
This means that either the mass is zero (which is not practical) or the acceleration must be zero.

4. **Analyzing Acceleration**: If acceleration is zero, it indicates that the object is either:
- At rest (not moving), or
- Moving with a constant velocity (maintaining the same speed and direction).

5. **Conclusion**: Therefore, for an object to be in equilibrium, it must satisfy one of the following conditions:
- The object is at rest.
- The object is moving with a constant velocity.

6. **Evaluating Options**: Based on the conditions derived, we can evaluate the given options:
- Option A: Only at rest (incorrect)
- Option B: Only moving with constant velocity (incorrect)
- Option C: Only moving with constant acceleration (incorrect)
- Option D: Either at rest or moving with constant velocity (correct)

Thus, the correct answer is **Option D**.