Assertion: A quick collisions between two bodies is more violent than a slow collisions even when the initial and the final velocities are identical
Reason: Because the rate of change of momentum which determines the force is greater in the first case.

Options

A. IF both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If assertion is false but reason is true

Explanation

To solve the assertion and reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that a quick collision between two bodies is more violent than a slow collision, even when the initial and final velocities are identical.

**Explanation:**
- A quick collision implies that the time duration of the collision (Δt) is very short.
- A slow collision implies that the time duration of the collision is longer.
- Even if both collisions start and end with the same velocities, the nature of the collision (quick vs. slow) affects how the forces are experienced during the collision.

### Step 2: Understanding the Reason
The reason provided states that the rate of change of momentum, which determines the force, is greater in the case of a quick collision.

**Explanation:**
- The rate of change of momentum (force) can be expressed mathematically as:
\[ F = \frac{\Delta p}{\Delta t} \]
where Δp is the change in momentum and Δt is the time duration of the collision.
- For both quick and slow collisions, the change in momentum (Δp) is the same (since the initial and final velocities are identical).
- However, in a quick collision, Δt is smaller, which means that the force (F) is greater because the same change in momentum occurs over a shorter time.

### Step 3: Conclusion
Both the assertion and the reason are true. The assertion correctly describes the nature of quick and slow collisions, and the reason accurately explains why quick collisions are more violent due to a greater rate of change of momentum.

### Final Answer
- **Assertion:** True
- **Reason:** True
- **Conclusion:** The reason correctly explains the assertion.

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