Final answer:
Displacement in one-dimensional motion like that of a subway train involves both magnitude and direction. Using the equation Δx = x - xo, positive displacement indicates movement to the right, while negative displacement indicates movement to the left. The magnitude is the absolute value of the change in position.
Step-by-step explanation:
Magnitude and Sign of Displacements in Subway Train Motion
When addressing the problem of calculating the displacement of a subway train, it is essential to consider both the magnitude and the sign of the displacement to fully understand the motion. Displacement, often represented as Δx, is the difference between the final position and the initial position of an object and is vector in nature, meaning it has both magnitude and direction. In one-dimensional motion scenarios like subway train movement, the use of positive and negative signs is paramount in indicating direction.
To find the displacement of the subway train from Figure 2.18 part (a), where the train moves to the right, and from part (b), where the train moves to the left, you will use the equation Δx = x - xo. Here, x represents the final position, and xo represents the initial position. If the train moves to the right, which we can consider as the positive direction, any displacement in that direction will be positive. Conversely, if the train moves to the left, the displacement will be negative, indicating the opposite direction.
For a train moving to the right and ending further to the right from where it started, the displacement will be a positive value. If the train moves to the left and ends further to the left from where it started, the displacement will also be a positive value since direction is already accounted for by the negative sign. The magnitude of displacement is just the absolute value of this change, regardless of direction.