In an elastic collision

Options

A. the initial kinetic energy is equal to the final kinetic energy
B. thefinal kinetic energy is les than the initial kinetic energy
C. the kinetic energy remains constnt
D. the kinetic energy first increases then decreases

Answer

### Step-by-Step Solution:

1. **Understanding Elastic Collision**: In an elastic collision, two objects collide and then separate without any loss of kinetic energy. The total kinetic energy before the collision is equal to the total kinetic energy after the collision.

2. **Initial Kinetic Energy**: Let’s denote the initial kinetic energies of the two colliding objects as \( KE_{initial} \). For two objects with masses \( m_1 \) and \( m_2 \) and initial velocities \( v_1 \) and \( v_2 \), the initial kinetic energy is given by:
\[ KE_{initial} = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 \]

3. **Collision Process**: During the collision, the two objects may deform temporarily, converting some of their kinetic energy into potential energy associated with the deformation. However, this potential energy is not lost; it is converted back into kinetic energy when the objects return to their original shape.

4. **Final Kinetic Energy**: After the collision, the objects will regain their shape and size, and the kinetic energy will be restored. Thus, the final kinetic energy \( KE_{final} \) can be expressed as:
\[ KE_{final} = \frac{1}{2} m_1 v_1'^{2} + \frac{1}{2} m_2 v_2'^{2} \]
where \( v_1' \) and \( v_2' \) are the final velocities of the two objects after the collision.

5. **Equating Initial and Final Kinetic Energy**: Since no kinetic energy is lost in an elastic collision, we have:
\[ KE_{initial} = KE_{final} \]
Therefore, the correct statement regarding kinetic energy in an elastic collision is that the initial kinetic energy is equal to the final kinetic energy.

6. **Conclusion**: The correct answer is that in an elastic collision, the initial kinetic energy is equal to the final kinetic energy.