Displacement Meaning in Physics
A study generally performed on the displacement of the object is the displacement mechanics.
We all like to take a shortcut in our lives or while driving to our office while getting late, so the shortest path we take is displacement.
A displacement is a vector form of the shortest distance between the initial position and the final position.
On this page, also we will discuss what is displacement, displacement definition, displacement meaning in Physics, displacement of the particle, be it having a linear motion or the circular motion.
What Is Displacement?
If you are curious to know what displacement is, look at the following diagram:
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Let’s suppose that the distance between points A and B is 30 m and the shortest path between these points is along the way, which is just 16 m from your destination. If you are asked which path you will choose?
Definitely, you will travel through the 16 m path line, so this path line is the displacement (this is the displacement definition).
Displacement Definition Physics
Now, let us understand the displacement definition with the help of a known term ‘distance’:
Example 1:
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Soham walks from point A to B to C. What distance, does he travel? What is the displacement?
Let's first calculate the distance Soham travels. While calculating distance, we look at the numerical value of the distance interval between the travelled points. As we can see from the above figure that he travels from A to B, then B to C. Distance from point A to B is 4m and from B to C is 3 m. So, their sum will give us total distance as;
4 m + 3 m = 7 m
Now, it's time to calculate displacement. Since displacement is a vector quantity, so it has both magnitude and direction.
In our stated example, the initial point is A and the final point is C. Displacement vector is an interval between the initial and final points. As it can be clearly seen that the interval between A to C is 5m. So, our displacement vector is 5m and its direction is from point A to C.
Let’s look at another example:
Example 2:
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We find distance taken by an object as;
From A to B =10 - 2 = 8m
From B to C = 10 - 2 = 8m
Then, from C to D = 10 - 6 = 4m
Total distance traveled from point A to point D is;
=> 8m + 8m + 4m = 20m
Now, we can find the final displacement by drawing a straight line from point A to the final point F. As we can see from the above graph, the object changes its position to 8m. So, the displacement is given as;
Displacement = Final position - Initial position
Displacement = 10m - 2m = 8m
Displacement Mechanics
Now, let us understand the displacement mechanics with the help of the below diagram:
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Look at the image above, you can see there are two multiple paths between point P’ and P. Now, the distance that lies very close to both is indicated by the path line. This path line is nothing but displacement.
Since displacement is indicated by a direction with the magnitude, we call this quantity a vector. A displacement vector is represented by an arrow-head, where an arrow indicates the direction and the tail follows it.
Here, we considered a field of displacement to represent the displacement mechanics, now let’s understand the displacement field.
Mechanical Displacement
A displacement field is assigning the displacement vectors for all points in a region for a body that is displaced from one position to another.
A displacement vector specifies the position of the displacement of a particle in reference to an origin or to a previous position.
For example, a displacement field may be used to describe the effects of deformation on a solid body that we study in the concept of stress and strain.
Before discussing displacement, the position before deformation must be defined. It is a state in which the coordinates of all points are known and described by the following function:
Po➝: Ω ->Q ….(1)
Where
Po➝ is a displacement vector
are all the points of the body
Q are all the points in the space in which the body resides
Force Into Displacement
In the above equation (1), we understand that the displacement vectors point to all the directions of an object.
Most often it is a state of the body in which no force to displacement is applied, then given any other state of this body in which coordinates of all its points are described in the following manner:
v➝ = P1➝ - Po➝…..(2)
From the above equation (2), we can see that the displacement field is the difference between two body states or positions.
and, v➝ is a displacement field, which for each point of the body specifies a displacement vector.
FAQs on Displacement Mechanics
1. What is displacement in the context of Physics?
In Physics, displacement is defined as the change in the position of an object. It is a vector quantity, which means it has both magnitude (size) and direction. It represents the shortest straight-line distance from the initial point to the final point, along with the direction of motion.
2. How is displacement fundamentally different from distance?
Displacement and distance are two distinct concepts in mechanics:
- Nature: Displacement is a vector quantity (magnitude and direction), while distance is a scalar quantity (magnitude only).
- Path Dependence: Displacement depends only on the initial and final positions, not the path taken. Distance is the total length of the actual path travelled.
- Value: Displacement can be positive, negative, or zero. Distance is always positive and non-zero if motion has occurred.
For example, if you walk around a 400m circular track and return to your starting point, your distance travelled is 400m, but your displacement is zero.
3. What is the SI unit and the general formula for calculating displacement?
The SI unit for displacement is the metre (m), the same as for distance. The formula for displacement (Δx) is the difference between the final position (x_f) and the initial position (x_i):
Δx = x_f - x_i
Here, the result's sign indicates the direction relative to the origin.
4. Why is it crucial to understand that displacement is a vector and not a scalar?
Understanding displacement as a vector is crucial because many other important physical quantities in mechanics, such as velocity and acceleration, are derived from it. Velocity is the rate of change of displacement (not distance), and acceleration is the rate of change of velocity. Without the directional information provided by the displacement vector, we cannot accurately describe an object's motion, predict its future position, or calculate forces acting upon it using Newton's laws.
5. Can the magnitude of displacement ever be greater than the distance travelled? Explain why or why not.
No, the magnitude of displacement can never be greater than the distance travelled. Displacement represents the shortest possible path—a straight line—between two points. The distance is the length of the actual path taken, which can be curved, zigzag, or indirect. Therefore, the distance is either equal to the magnitude of the displacement (if the motion is in a straight line without changing direction) or greater than it.
6. How does the concept of a 'displacement field' extend the idea of simple displacement?
A displacement field is a more advanced concept used in continuum mechanics to describe the deformation of a solid body. Instead of tracking the displacement of a single point, a displacement field is a vector field that assigns a unique displacement vector to every point within the body. This field effectively maps how the entire body has moved and deformed from its initial configuration to its final one, which is essential for analysing concepts like stress and strain.
7. How is displacement represented on a position-time graph and what can be inferred from it?
On a position-time graph, displacement is represented by the change in the vertical axis (position) between two points in time. For any time interval, the displacement is the final position coordinate minus the initial position coordinate. Key inferences from the graph include:
- A horizontal line indicates zero displacement (the object is stationary).
- A straight, sloped line indicates constant velocity.
- The slope of the line connecting two points on the graph gives the average velocity during that time interval.
