In physics, mechanics includes the study of the object’s motion. Kinematics is the branch of mechanics science that describes the motion of objects with the use of some terms, diagrams, graphs, numbers, and equations. These are also described by mathematical quantities which are used for determining the motion of objects. These are divided into two types that are a vector or a scalar which can be distinguished by their particular definitions which shows that **Scalars quantities** are easily represented by a magnitude or their numerical value while **vectors quantities** are described by use of both a magnitude and a direction.

Some examples of these quantities are acceleration, distance, speed, displacement, velocity etc. If we discuss distance and displacement are two quantities out of which distance is scalar quantity while displacement is vector quantity which shows the change in position of object but the distance shows the covered length by moving object. When we travel from one location to other location for reach fast on the destination, we take shortcuts making distance less so we prefer straight path over curved path. So these two quantities are related to the motion of object. Here we discuss all about the displacement.

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Displacement is that what tells about the change in position. It is a vector and is the overall change in the position from the reference point. It is the shortest distance between the initial point and the final point. It prefers straight line path over curved path and is a vector quantity.

From these definitions, it is not yet clear what the difference between the distance and the displacement is? For understanding the difference between these quantities we must look at the following example.

From these definitions, it is not yet clear what the difference between the distance and the displacement is? For understanding the difference between these quantities we must look at the following example.

Example:

A person has walked as follows (i) For the first 10 seconds, he walked to the north for 100 meters.
(ii) For the next 30 seconds, he turns west and walks for 200 meters.
(iii) For the next 10 seconds, he turns north and walks for 300 meters.
(iv) Find the distance and displacement of the person from its original place.

To understand it, we need to look at the picture below:

From the figure, if we want to find the displacement, it is the overall distance from the initial point (a) to the final point (B), which
is 400 meters only, i.e. the direct distance between **A** and **B**.

From this example, we can conclude that**displacement is the shortest distance between two points.**

From this example, we can conclude that

There is no single formula for displacement, it depends on the other quantities present in the problem. Still, there are a few formulae using which we can find the displacement.

S = vt

S = ut + $\frac{1}{2}$at^{2}

where u and v are initial and final velocity and a is acceleration.S = ut + $\frac{1}{2}$at

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- The Distance as already discussed is the scalar quantity and it is the total path or actual path covered by the object between initial and the final point.The displacement is the shortest path between two points and it is the vector quantity.
- Both are measured in unit of lengths. Distance is generally associated with the speed of the body while displacement with the velocity of the body.
- The distance is also said to be the magnitude of displacement.

When an object is moving in a circular or curved path, its displacement is measured as the change of angle from its initial position to the final position. This displacement is known as **angular displacement**. It is measured in **radians**.

The relation between linear displacement and angular displacement isThe angular displacement is given by $\theta$
where **$\theta$** is the angle between initial and final position of the object moving in Curved path.

→ Read More Let us consider the motion of an object from point

The 'Resultant' term itself means the Sum or Total. So, the term Resultant displacement is the sum of all the displacements which have taken place.

From the above discussion we know that the displacement is the vector quantity, i.e., it has both magnitude and direction. If displacement is negative, it does not mean that the displacement is getting decreased, it means that the displacement is taking opposite direction. And hence the **negative sign** indicates that the object is moving in the opposite direction with respect to its initial position.

Following are the solved problems which will help you know more about the displacement.

While traveling to the east it covered a distance of 300 meters (10 $\times$ 30 = 300) and when it turns left it is moving in north direction for another 30 seconds so the distance it covers in north direction is 200 meters (10 $\times$ 40 = 400). The figure of this motion is as shown:

Since the figure is Right angled triangle, the resultant displacement will be,

AB = $\sqrt{AO^{2} + OB^{2}}$

= $\sqrt{300^{2} + 400^{2}}$

= 500 m.

His resultant displacement is given by :

S = $\sqrt{400^{2}+700^{2}}$

S = $\sqrt{160000 + 490000}$

S = $\sqrt{650000}$

S = 806.23 meters.

Although his total distance traveled is 1100 meters but his resultant displacement is 806.23 meters in North – West direction.

1. Total distance traveled by the bus is D = 100 + 200 = 300 km.

2. Magnitude of the displacement is,

|S| = $\sqrt{100^{2} + 200^{2}}$,

= $\sqrt {50000}$,

|S| = 223.61 kms.

3. Direction of the resultant displacement is, the bus travels first to south and then turns left so it turns in west and hence the resultant direction from the city A is south – west.

1. Total distance covered by him is: 100 + 200 + 50 = 350 meters.

2. Magnitude of the displacement can be obtained by visualizing his walking,

The distance from A to B is 100 meters,

from B to C is 200 meters and from C to D is 50 meters.

So, the magnitude of resultant displacement is,

|S| = $\sqrt{50^{2} + 200^{2}}$

= $\sqrt{42500}$

|S| = 206.155 m.

3. The direction of the resultant displacement is South–West.

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Angular Displacement | |

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