In an elastic collision

Options

A. the kinetic energy remains constant
B. the linear momentum remains constant
C. the final kinetic energy is equal to the initial kinetic energy
D. the final linear momentum is equal to the initial linear momentum

Answer

To solve the question regarding elastic collisions, we need to analyze the properties of such collisions in terms of kinetic energy and linear momentum.

### Step-by-Step Solution:

1. **Understanding Elastic Collision**:
An elastic collision is defined as a collision in which both kinetic energy and linear momentum are conserved. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision, and the total linear momentum before the collision is equal to the total linear momentum after the collision.

2. **Conservation of Kinetic Energy**:
In an elastic collision, the kinetic energy does not change. Mathematically, this can be expressed as:
\[ KE_{\text{initial}} = KE_{\text{final}} \]
This means that the total kinetic energy of the system remains constant throughout the collision.

3. **Conservation of Linear Momentum**:
Similarly, the linear momentum of the system is conserved. This can be expressed as:
\[ p_{\text{initial}} = p_{\text{final}} \]
where momentum \( p \) is defined as the product of mass and velocity.

4. **Final Statements**:
Therefore, in an elastic collision, we conclude that:
- Kinetic energy remains constant.
- Linear momentum remains constant.
- Final kinetic energy equals initial kinetic energy.
- Final linear momentum equals initial linear momentum.

### Conclusion:
In summary, all the statements regarding elastic collisions are true:
- Kinetic energy remains constant.
- Linear momentum remains constant.
- Final kinetic energy equals initial kinetic energy.
- Final linear momentum equals initial linear momentum.