A physics book is moved once around the perimeter of a table of dimensions 1 meter by 2 meters. if the book ends up at the initial position, what is its displacement? what is the distance traveled?

In our case, we are to solve for the displacement and distance of a book around a rectangular table. Displacement is a vector, so we are to consider magnitude and direction in solving for it. Now, distance is scalar so we are just going to solve for its magnitude. In solving for the distance, we will just add all the given sides of the rectangle.

To solve for the displacement, we are to apply Pythagorean theorem using this formula:

d² = (∑x)² + (∑y)²

Let us assume that from the starting point, it moves 2m to the right then 1m downward then 2m to the left and finally 1 m upward.

∑x: 2m to the right, 2m to the left

∑y: 1m downward, 1m upward

Take note that we:

+ for upward and to the right directions

- for downward and to the left directions

1. Let us solve for the displacement.

∑x = 2m - 2m = 0

∑y = 1m - 1m = 0

d² = (∑x)² + (∑y)²

d = 0

2. Now, let us solve for the distance. We can add all the given sides of the rectangle or perimeter of it.

For the formula for the perimeter of the rectangle, we have:

P = 2L + 2W

Then substitute the given information, we have:

P = 2(2 m) + 2(1 m)

P = 4m + 2m

P = 6m

Therefore, the total distance traveled by the book is 6m.

Therefore, the displacement of the book is zero and the distance is 6m.

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