Final answer:
The total distance traveled by the vehicle is 109 km. To calculate displacement, we find the net east-west and north-south travel and use the Pythagorean theorem, which gives us a displacement of approximately 31 km southeast. None of the multiple-choice options provided are correct.
Step-by-step explanation:
The total distance traveled by a vehicle and its displacement are two different quantities in physics. Distance is the total length of the path traveled regardless of direction, while displacement is the shortest path between the start and end points in a specific direction.
To calculate the total distance, we add up all segments: 10 km east + 15 km south + 20 km west + 19 km east + 15 km north + 30 km south = 109 km. The displacement is found by calculating the net distance covered in each direction: Final East-West position = 10 km east + 19 km east - 20 km west = 9 km east; Final North-South position = 30 km south + 15 km south - 15 km north = 30 km south. The displacement vector, therefore, has components 9 km east and 30 km south.
To find the magnitude of displacement, we use the Pythagorean theorem: \(\sqrt{(9 km)^2 + (30 km)^2}\), which equals approximately 31 km southeast. Hence, the vehicle's total distance traveled is 109 km, and the displacement is approximately 31 km southeast.
The correct answer to the student's question is: None of the given options match the calculated values. The total distance traveled is 109 km, but the displacement is approximately 31 km southeast, not mentioned in the choices.