Final answer:
To find the velocity with which the middle point of a uniformly accelerating train passes a signal post, we take the average of the initial and final velocities, resulting in (u + v) / 2.
Step-by-step explanation:
The question involves the concepts of uniform acceleration and velocities of an object at different points in time. When an engine with uniform acceleration passes different points, like a signal post or the end of a train, it exhibits different velocities.
To find the velocity with which the middle point of the train passes the signal post, we use the concept that the average velocity, when acceleration is constant, is equal to the mean of the initial and final velocities.
Therefore, the velocity with which the middle point of the train passes the signal post is given by:
vmiddle = (u + v) / 2
Here, the correct answer would be (a) (u + v) / 2, considering that uniform acceleration is present and we are taking the arithmetic mean of the two velocities.
This relates to the idea that the middle position would correspond to the midpoint in the train's velocity-time graph, which would be the average of the initial and final velocities.