To determine the midpoint velocity of a train when the engine has an initial velocity 'u' and the last coach crosses a pole at velocity 'v', basic kinematic equations can be applied. The midpoint velocity can be calculated as an average of the initial and final velocities of the train. Since the guard's coach is moving at 'v', it suggests that the velocity of the midpoint will be influenced by both 'u' and 'v'. The assumption that the midpoint velocity equals 'v' is incorrect without considering acceleration or deceleration. Therefore, the correct approach involves using the average of the two velocities to find the midpoint velocity at that instant.