A book is moved once around the edge of a tabletop with dimensions 1.75m x 2.25m. If the book ends up at the initial position, what is its displacement? If it completes its motions in 23s, what is its average velocity? What is its average speed?
To find the displacement of the book, we need to calculate the straight-line distance between the initial and final positions. We can use the Pythagorean theorem to calculate the displacement.
Given the dimensions of the tabletop, the length is 2.25m and the width is 1.75m. Since the book ends up at the initial position, it completes a rectangular path around the edge of the tabletop.
To find the displacement, we can calculate the length of all four sides of the rectangle and then sum them up.
The distance along the longer side (2.25m) is covered twice, once on the initial run and once on the return run. So, the total distance covered along the longer side is 2 * 2.25 = 4.5m.
Similarly, the distance along the shorter side (1.75m) is also covered twice. So, the total distance covered along the shorter side is 2 * 1.75 = 3.5m.
Adding up these distances, we get the total displacement: 4.5m + 3.5m = 8m.
Therefore, the displacement of the book is 8 meters.
To calculate the average velocity, we divide the displacement by the time taken. The displacement of the book is 8m, and it completes its motion in 23s.
Average velocity = Displacement / Time
Average velocity = 8m / 23s
Average velocity ≈ 0.348 m/s (rounded to three decimal places)
Therefore, the average velocity of the book is approximately 0.348 m/s.
To calculate the average speed, we divide the total distance covered by the time taken. Since the book moves along a rectangular path, we need to calculate the perimeter of the rectangle.
The perimeter of the rectangle is 2 * (length + width) = 2 * (2.25m + 1.75m) = 2 * 4m = 8m.
Average speed = Total distance / Time
Average speed = 8m / 23s
Average speed ≈ 0.348 m/s (rounded to three decimal places)
Therefore, the average speed of the book is approximately 0.348 m/s, which is the same as the average velocity.