Two trains going in opposite directions with the same speed are at rest relative to each other. True/False.

Answer

To determine whether the statement "Two trains going in opposite directions with the same speed are at rest relative to each other" is true or false, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have two trains, Train A and Train B.
- Train A is moving in one direction with a speed of \( v \).
- Train B is moving in the opposite direction with the same speed \( v \).

2. **Relative Speed Concept**:
- The relative speed between two objects moving in opposite directions is calculated by adding their speeds.
- Therefore, the relative speed \( v_{relative} \) between Train A and Train B can be expressed as:
\[ v_{relative} = v + v = 2v \]

3. **Conclusion on Relative Motion**:
- Since the relative speed \( v_{relative} \) is \( 2v \), this means that from the perspective of a person on Train A, Train B appears to be moving at a speed of \( 2v \).
- Consequently, the two trains are not at rest relative to each other.

4. **Final Answer**:
- The statement "Two trains going in opposite directions with the same speed are at rest relative to each other" is **False**.