Question

Which has the greater displacement, object 1 , which moves from \(5.0 \mathrm{~m}\) to \(7.0 \mathrm{~m}\) in \(2.0 \mathrm{~s}\), or object 2 , which moves from \(15 \mathrm{~m}\) to \(16 \mathrm{~m}\) in \(25 \mathrm{~s}\) ? Explain.

Short answer

Object 1 has the greater displacement (2.0 m).

Step-by-step solution

Understand Displacement

Displacement is defined as the change in position of an object. It is calculated as the final position minus the initial position.

Calculate Displacement for Object 1

For object 1, the initial position is \(5.0 \, \text{m}\) and the final position is \(7.0 \, \text{m}\). The displacement is calculated as follows: \[ \text{Displacement}_1 = 7.0 \, \text{m} - 5.0 \, \text{m} = 2.0 \, \text{m} \]

Calculate Displacement for Object 2

For object 2, the initial position is \(15 \, \text{m}\) and the final position is \(16 \, \text{m}\). The displacement is calculated as follows: \[ \text{Displacement}_2 = 16 \, \text{m} - 15 \, \text{m} = 1.0 \, \text{m} \]

Compare the Displacements

Compare the displacements calculated for the objects. Object 1 has a displacement of \(2.0 \, \text{m}\) while object 2 has a displacement of \(1.0 \, \text{m}\).

Key concepts

Change in Position

When we discuss displacement in physics, what we really mean is the change in position of an object. Position refers to the specific location of an object in space. As an object moves, its position changes from a starting point to an end point. This change can be through space in any direction.

This change in position is what we call displacement. It's important to note that displacement is not concerned with the path taken—rather, it focuses solely on the initial and final positions. Therefore, regardless of how an object travels between these two points, its displacement will remain the same if the start and end points are unchanged. If you imagine drawing a straight line from where an object starts to where it finishes, that is essentially the displacement.

• Initial position: where an object begins.
• Final position: where the object ends up.
• Displacement: final position - initial position.

The simplicity of considering only the start and end points makes understanding the concept of displacement straightforward.

Calculation of Displacement

To calculate displacement, you will subtract the initial position from the final position. This tells you how much distance and in which direction an object has moved.

For instance, consider Object 1 in this exercise. Its initial position is at 5.0 meters, and its final position is at 7.0 meters. So, the displacement for Object 1 would be:\[ \text{Displacement}_1 = 7.0 \, \text{m} - 5.0 \, \text{m} = 2.0 \, \text{m} \]For Object 2, which starts at 15 meters and moves to 16 meters, its displacement calculation would be:\[ \text{Displacement}_2 = 16 \, \text{m} - 15 \, \text{m} = 1.0 \, \text{m} \]The subtraction tells us how far and in which direction the object has moved from the starting point. Notice that these calculations ignore any time taken or the specific path traveled. That simplicity is a strength of using displacement for many physics problems. It purely accounts for the change between initial and final positions.

Comparison of Displacements

Comparing displacements enables us to understand which object has had a greater change in position. In our problem, Object 1 has a displacement of 2.0 meters, while Object 2 has a displacement of only 1.0 meter.

This comparison is straightforward: the object with a greater numerical value of displacement has undergone a larger shift from its starting to its ending position.

• Displacement of Object 1: 2.0 m
• Displacement of Object 2: 1.0 m

In conclusion, Object 1 experiences a greater displacement because it moved 2.0 meters between its initial and final position, whereas Object 2 only moved 1.0 meter. This concept is crucial in physics, as it allows you to quantify and compare how much movement occurred between objects regardless of how the movement took place.