How to Find Total Displacement in Physics
Displacement is a fundamental concept in physics that refers to the change in position of an object. It is an important quantity when analyzing the motion of objects, as it helps us understand the distance and direction an object has moved. In this article, we will discuss how to find the total displacement of an object in physics.
Understanding Displacement
Before we delve into the calculation of total displacement, it is crucial to understand what displacement is. Displacement is a vector quantity, meaning it has both magnitude and direction. It is the shortest distance between the initial and final positions of an object. To calculate the displacement, we need to know the initial position, the final position, and the direction of the motion.
Step-by-Step Guide to Finding Total Displacement
1. Determine the initial position: The initial position is the starting point of the object’s motion. It is usually represented by a point in space, often with coordinates (x1, y1, z1).
2. Determine the final position: The final position is the ending point of the object’s motion. Similar to the initial position, it is also represented by a point in space, often with coordinates (x2, y2, z2).
3. Calculate the difference in position: To find the displacement, we need to calculate the difference between the final and initial positions. This can be done by subtracting the initial coordinates from the final coordinates:
Δx = x2 – x1
Δy = y2 – y1
Δz = z2 – z1
4. Find the magnitude of the displacement: Once we have the differences in the x, y, and z coordinates, we can calculate the magnitude of the displacement using the Pythagorean theorem:
|Δr| = √(Δx² + Δy² + Δz²)
5. Determine the direction of the displacement: The direction of the displacement is the angle between the displacement vector and the positive x-axis. To find this angle, we can use the arctangent function:
θ = arctan(Δy / Δx)
Note that the angle θ will be in radians. If you need the angle in degrees, you can convert it using the following formula:
θ_degrees = θ_radians (180 / π)
Example
Let’s consider an example to illustrate the process of finding total displacement. Suppose an object starts at the point (2, 3, 4) and moves to the point (8, 7, 6). To find the total displacement, we follow these steps:
1. Initial position: (2, 3, 4)
2. Final position: (8, 7, 6)
3. Calculate the difference in position:
Δx = 8 – 2 = 6
Δy = 7 – 3 = 4
Δz = 6 – 4 = 2
4. Find the magnitude of the displacement:
|Δr| = √(6² + 4² + 2²) = √(36 + 16 + 4) = √56 ≈ 7.48
5. Determine the direction of the displacement:
θ = arctan(4 / 6) ≈ 0.927 radians
So, the total displacement of the object is approximately 7.48 units in the direction of 0.927 radians from the positive x-axis.
