Macy is playing with her toy train. She is pushing it along a wood track. The train starts its journey 15 cm to the left of the station. She travels 90 95 cm to the right of the station and ends its journey directly in front of the station. If negative values are assigned to positions to the left of the starting position and the positive values are assigned to positions to the right of the starting position, what is the displacement of the train?

Answer 1

To determine the displacement of Macy's toy train, we first need to establish its initial and final positions based on the information provided.

1. The starting position of the train is 15 cm to the left of the station, which can be represented as: \[ \text{Initial Position} = -15 , \text{cm} \]

2. The train travels a distance of 90.95 cm to the right of the station. Since the station is considered as the position 0 cm, the right direction is positive.

   • Traveling 90.95 cm to the right from the station (0 cm) leads to a final position of: \[ \text{Final Position} = 0 + 90.95 = 90.95 , \text{cm} \]

However, the problem states the train ends its journey directly in front of the station, which means the final position is actually: \[ \text{Final Position} = 0 , \text{cm} \]

3. Now we can calculate the displacement, which is defined as the change in position from the initial position to the final position: \[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \] Plugging in the values: \[ \text{Displacement} = 0 , \text{cm} - (-15 , \text{cm}) = 0 + 15 , \text{cm} = 15 , \text{cm} \]

Thus, the displacement of the train is: \[ \boxed{15 , \text{cm}} \]