The momentum of an object at a given instant is independent of its

Options

A. inertia
B. speed
C. velocity
D. acceleration

Explanation

To determine which factor the momentum of an object at a given instant is independent of, we can analyze the relationship between momentum and the other options provided.

### Step-by-Step Solution:

1. **Understanding Momentum**:
- Momentum (P) is defined as the product of an object's mass (m) and its velocity (v).
- The formula for momentum is:
\[ P = m \times v \]

2. **Analyzing the Options**:
- We have four options to consider: inertia, speed, velocity, and acceleration.

3. **Option 1: Inertia**:
- Inertia is the property of an object to resist changes in its state of motion and is directly related to mass.
- Since momentum depends on mass, it is not independent of inertia.
- **Conclusion**: This option is incorrect.

4. **Option 2: Speed**:
- Speed is the magnitude of velocity.
- Since momentum depends on velocity, and speed is a part of that, momentum is also dependent on speed.
- **Conclusion**: This option is incorrect.

5. **Option 3: Velocity**:
- Velocity is a vector quantity that includes both speed and direction.
- Since momentum is directly proportional to velocity, it is not independent of velocity.
- **Conclusion**: This option is incorrect.

6. **Option 4: Acceleration**:
- Acceleration is the rate of change of velocity with respect to time.
- There is no direct relationship between momentum and acceleration in the formula for momentum (P = m × v).
- It is possible for an object to have a high acceleration while having a low velocity, indicating that momentum can exist independently of acceleration.
- **Conclusion**: This option is correct.

### Final Answer:
The momentum of an object at a given instant is independent of **acceleration**.

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