Two cars are moving is one a same line dimension in opposite direction with the same speed v. The relative velocity of two cars w.r.t. each other is

Options

A. 2 v
B. v
C. `(v)/(2)`
D. Zero

Answer

To find the relative velocity of two cars moving in opposite directions with the same speed \( v \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Direction of Motion**:
- Let’s assume Car A is moving in the positive x-direction with a speed \( v \).
- Car B is moving in the negative x-direction with the same speed \( v \).

2. **Assign Velocity Values**:
- The velocity of Car A, \( V_A = v \) (positive).
- The velocity of Car B, \( V_B = -v \) (negative because it is moving in the opposite direction).

3. **Use the Relative Velocity Formula**:
- The formula for relative velocity of Car A with respect to Car B is given by:
\[ V_{\text{relative}} = V_A - V_B \]

4. **Substitute the Values**:
- Substitute the values of \( V_A \) and \( V_B \) into the formula:
\[ V_{\text{relative}} = v - (-v) \]

5. **Simplify the Expression**:
- Simplifying the equation gives:
\[ V_{\text{relative}} = v + v = 2v \]

6. **Conclusion**:
- The relative velocity of the two cars with respect to each other is \( 2v \).

### Final Answer:
The relative velocity of the two cars with respect to each other is \( 2v \).

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