A tube with cross sections at A and B , having areas of 4 mm^2 and...

Given that the water falls down and its speed decreases, the water must completely fill the tube. This implies that the flow is steady and the equation of continuity is applicable.

According to the equation of continuity, the volume flow rate $Q$ is constant across any cross-section of the tube:

$Q = A_A v_A = A_B v_B$

We are given:
Volume flow rate, $Q = 1 \text{ cm}^3 \text{ s}^{-1}$
Cross-sectional area at $A$, $A_A = 4 \text{ mm}^2 = 4 \times 10^{-2} \text{ cm}^2$

Substituting the given values to find the speed of water at $A$ ($v_A$):

$v_A = \dfrac{Q}{A_A}$

$v_A = \dfrac{1}{4 \times 10^{-2}}$

$v_A = 25 \text{ cm/s}$