Final answer:
The truck travels a total distance of 11.0 km. The magnitude of the truck's displacement is 2.0 km towards the west.
Step-by-step explanation:
When addressing the question of how far the truck traveled and its displacement, we consider both the total distance traveled and the net displacement. First, we need to add up all the distances the truck has traveled regardless of direction. The truck travels:
- 1.8 km due east
- 6.5 km due west
- 2.7 km due east again
The total distance is therefore 1.8 km + 6.5 km + 2.7 km = 11.0 km.
To find the magnitude and direction of the truck's displacement, we need to take into account the direction of each segment of the trip. Displacement is a vector quantity that describes the net change in position:
- The displacement for the eastward segments is 1.8 km + 2.7 km = 4.5 km east.
- The displacement for the westward segment is 6.5 km west.
The total displacement is 4.5 km east - 6.5 km west = -2.0 km (or 2.0 km west), where the negative sign indicates the displacement is towards the west. Therefore, the magnitude of the displacement is 2.0 km, and the direction is to the west.