A

Step 1: Identify the variables from the question. Let the upward velocity of the lift (A) be \( v_A = 2 \, \text{m/s} \) and the downward velocity of block (B) be \( v_B = 2 \, \text{m/s} \).
Step 2: In a system of pulleys, the velocities are related by the condition of constant string length. If one part of the string moves up, the other part must move down accordingly, considering the direction of movement.
Step 3: Since the lift moves upward and the block is moving downward, their velocities are directly related. The upward velocity of the lift (A) is equal to the downward velocity of the block (B). Therefore, using the relation of speeds, we find that the velocity of block B is also \( v_B = 2 \, \text{m/s} \). Hence, option A is the correct answer.