At time t = 0, two bodies A and B at the same point. A moves with constant velocity `upsilon` and B starts from rest and moves with constant acceleration. Relative velocity of B w.r.t. A when the bodies meet each other is

Options

A. `(upsilon)/(2)`
B. `(upsilon)/(3)`
C. `upsilon`
D. `2upsilon`

Explanation

To solve the problem, we need to analyze the motion of both bodies A and B and determine the relative velocity of B with respect to A when they meet.

### Step-by-Step Solution:

1. **Understanding the Motion of Body A**:
- Body A moves with a constant velocity \( V_A = \upsilon \).
- The distance traveled by A after time \( t \) is given by:
\[ S_A = V_A \cdot t = \upsilon t \]

2. **Understanding the Motion of Body B**:
- Body B starts from rest and moves with a constant acceleration \( A \).
- The initial velocity \( u_B = 0 \).
- The distance traveled by B after time \( t \) is given by the equation of motion:
\[ S_B = u_B \cdot t + \frac{1}{2} A t^2 = 0 + \frac{1}{2} A t^2 = \frac{1}{2} A t^2 \]

3. **Setting the Distances Equal**:
- Since both bodies meet at the same point, we can set their distances equal:
\[ S_A = S_B \]
\[ \upsilon t = \frac{1}{2} A t^2 \]

4. **Solving for Acceleration \( A \)**:
- Rearranging the equation gives:
\[ A t^2 = 2 \upsilon t \]
- Dividing both sides by \( t \) (assuming \( t \neq 0 \)):
\[ A t = 2 \upsilon \]
- Thus, we can express \( A \) as:
\[ A = \frac{2 \upsilon}{t} \]

5. **Finding the Velocity of Body B**:
- The velocity of body B at time \( t \) is given by:
\[ V_B = u_B + A t = 0 + A t = A t \]
- Substituting the value of \( A \):
\[ V_B = \left(\frac{2 \upsilon}{t}\right) t = 2 \upsilon \]

6. **Calculating the Relative Velocity of B with Respect to A**:
- The relative velocity of B with respect to A is given by:
\[ V_{BA} = V_B - V_A \]
- Substituting the known velocities:
\[ V_{BA} = 2 \upsilon - \upsilon = \upsilon \]

### Final Answer:
The relative velocity of B with respect to A when the bodies meet each other is:
\[ \boxed{\upsilon} \]