Final answer:
The distance traveled by Earth during a quarter year is 37.5 million km, while the displacement is 0. The total distance traveled during two years and half is 375 million km, and the displacement is also 0.
Step-by-step explanation:
The distance and displacement of Earth during a quarter year can be calculated as follows:
a. A Quarter Year:
Since there are 4 quarters in a year, the Earth completes one quarter of its orbit around the Sun in 3 months. To find the distance traveled, we can divide the total distance of Earth's orbit (150 million km) by 4. Therefore, the distance during a quarter year is 150 million km / 4 = 37.5 million km. However, the displacement is 0, as displacement only considers the change in position, and after one quarter year, Earth is back to its starting position with respect to the Sun.
b. Two Years and Half:
To find the distance and displacement during two years and half, we need to calculate the distance and displacement for each year separately. In two years, Earth completes two full revolutions around the Sun. Therefore, the distance traveled is 2 times the distance of Earth's orbit, which is 2 * 150 million km = 300 million km. However, the displacement is 0, as Earth returns to its starting position after two years. In half a year (6 months), Earth completes half of its orbit. Thus, the distance traveled is half of the distance of Earth's orbit, which is 150 million km / 2 = 75 million km. However, the displacement is also 0, as Earth returns to its starting position after half a year. To find the total distance and displacement, we can add up the distances and displacements for each period. Therefore, the total distance traveled during two years and half is 300 million km + 75 million km = 375 million km, and the total displacement is 0.