## How Can I Calculate The Magnitude Of Displacement

#”Please study the animations and drawings carefully.”#

#### Explanation:

- think of a point P on the curvilinear path that moves from point A to point B.
The movement of the P point can be described by a reference point.

That reference point is O .

The coordinates of points A and B are # # ## respectively.

Now let’s draw a vector pointing to the first position of the P point. This vector is the position vector.

As the dot moves, the length and direction of the vector change.

We describe the change in the position of the point P with a vector because the displacement takes place in a certain direction.

This vector is represented by green color.

the magnitude of the displacement vector can be calculated by various methods.

We can use the Pythagorean theorem in the ABC triangle.

- #|o|=sqrt^2+^2)#

## Misconception Alert: Distance Traveled Vs Magnitude Of Displacement

It is important to note that the *distance traveled*, however, can be greater than the magnitude of the displacement . For example, the professor could pace back and forth many times, perhaps walking a distance of 150 m during a lecture, yet still end up only 2.0 m to the right of her starting point. In this case her displacement would be +2.0 m, the magnitude of her displacement would be 2.0 m, but the distance she traveled would be 150 m. In kinematics we nearly always deal with displacement and magnitude of displacement, and almost never with distance traveled. One way to think about this is to assume you marked the start of the motion and the end of the motion. The displacement is simply the difference in the position of the two marks and is independent of the path taken in traveling between the two marks. The distance traveled, however, is the total length of the path taken between the two marks.

## How To Calculate The Magnitude Of A Vector

Vector quantities also have magnitude but come with directions.

Some of the vector quantities are displacement, acceleration, velocity, force, and many more.

The magnitude of a vector can be called its absolute value.

In the case of vectors, two or more vectors can only be equal if they have the same magnitude and direction.

If the vector is multiplied with a positive integer, the magnitude of a vector changes while its direction will remain constant.

Similarly, we multiply any vector with a negative integer, the direction, and magnitude of the vector change.

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## Examples Of Displacement And Distance

Now with this brief definition, we can go further and explain those concepts more concisely with numerous examples.

**Example : A boy playing around a rectangle. He starts his game from one corner and ends at the same one. **

**Solution:** In this path, since his initial and final points are the same so, by definition, __his displacement is zero__.

On the other hand, the __total distance traveled by him is the perimeter__ of that rectangular shape.

In this way, distance traveled is consistent with the concept of displacement in everyday language.

**Example : A biker ride into a horizontal loop of a radius of 10 meters and covers three fourth of it as follows. What are the displacement and distance traveled by him?**

**Solution:** As mentioned earlier, displacement is a quantity that depends only on the position of initial and final points.

Thus, the straightest line between those points, which gives the magnitude of the displacement vector, are computed by Pythagorean theorem as\begin D^ & =& r^ + r^ \\ & =& 2\, r^ \\ \Rightarrow D & =& r\, \sqrt \end where the magnitude of displacement denoted by $D$. Putting the values gives, $D\, = \, 10\sqrt\, $.Distance is simply the circemference of three fourth of the circle, so \begin \text & =& \frac \, } \\\\ & =& \frac \left \\\\ & =& \frac \\\\ & =& 15\,\pi \, \end

**Example : A person starts at position 0 and walks 4 meters to the right, returns and walks 6 meters to the left. What is displacement? What is the distance traveled by him?**

## Distance And Displacement With Examples

**Distance and Displacement**

** Distance** is a scalar quantity representing the interval between two points. It is just the magnitude of the interval. However,

**is a vector quantity and can be defined by using distance concept. It can be defined as distance between the initial point and final point of an object. It must be the shortest interval connecting the initial and final points, that is a straight line.Let’s look at the below examples for deep understanding.**

*Displacement*Look at the picture above, boy travels from D to A, A to B, B to C and C to D. Displacement from D to D is zero. However, distance traveled is not zero. It is equal to the perimeter of the rectangle.

Another example of distance and displacement is illustrated in Figure 1.2

John walks from the point A to B to C. What does the distance he travel? What is the displacement?

Let’s calculate first the distance that john travels. While calculating distance, we look at the numeric value of interval between traveled points. As you can see from Figure 1.2 he travels from A to B to C. Distance from A to B is 4m and B to C is 3 m. Their sum will give us total distance

**4+3=7**

**Example:** Look at the picture given below. An object moves from point A through B, C, D, E and stops at point F.

a) Find final displacement.

b) Find distance taken from point A to D.

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## Definition Of Displacement And Distance

Displacementis a vector quantity describes a change in position of an object or how far an object is displaced from its initial position and is given by below formula \Where the starting and ending positions are denoted by $x_i$ and $x_f$, respectively.Distanceis a scalar quantity indicating the total path traveled by a moving object.

Since in both cases, the interval between two points is measured- one as the shortest line and the other as the total traveled path- so the SI unit of displacement and distance is the meter. The illustration below shows the difference between them clearly.

## How To Calculate Net Displacement

Suppose a particle moves several times. The **net displacement** is the displacement vector between the particles initial position and the final position. The net displacement can also be obtained by vector addition of each of the individual displacement vectors that corresponds to each stage of motion. For example, in the diagram below, the position vector of the point is and the position vector of the point is .

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## How Do Double Displacement Reactions Work

A double displacement reaction, also known as a double replacement reaction or metathesis reaction, is a type of reaction that occurs when the cations and anions switch between two reactants to form new products. After that, we switch the ions of the two reactants and write down the products.

## Difference Between Distance And Displacement

Let us now look at the differences between distance and displacement.The first one is the displacement of an object may be zero but the distance traveled by the object is never zero.To explain this further again consider that in our example the man travels to point A, then to point B and finally returned to reference point O then

Now, displacement, in this case, would be zero since O is the initial as well as the final position of the man.Again, if any object is moving along a circular path, starts at point A and return to point A then the total distance covered would be \ but the net displacement of the object would be zero. So,

* Distance traveled by a moving body cannot be zero but the final displacement of a moving body can be zero*.

We have also discussed earlier that displacement of an object can be negative but distance traveled by an object can never be negative.Another difference between distance and displacement is that

*Distance is a a scalar quantity that is it only has magnitude and no direction is specified*.

Whereas displacement is a vector quantity as it has both magnitudes and direction.For example, if a car travels a distance of 60 Km then this 60 kilometer is the distance traveled.Again, if the car is moving in straight line towards west then the displacement of the car of the car would be expressed as 50 kilometer towards west.

**Watch this video on position, distance and displacement for a clear idea.**

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## What Does Net Displacement Mean

**4.4/5****is****means displacement is****is****net displacement**read full answer

The **net** **displacement** is the vector sum of two displacements: the first **displacement** and the second **displacement** : The easiest way to find the **net displacement** is to introduce coordinate system and then find the x and y components of the **net** vector-**displacement**.

Furthermore, what does negative displacement mean? **Negative displacement means** distance in the **negative** direction. So, instead of 10 m forward from the origin, it’s 10 m backward from the origin.

Consequently, what is the rule for displacement?

In geometry, a **displacement** is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. For motion over a given interval of time, the **displacement** divided by the length of the time interval defines the average velocity.

Why do we need displacement?

In case **we want** to know the average velocity during a given interval of time, **we would need** to take the difference of final position of the body and its initial position. This difference in positions **is** the **displacement** of the body. **Displacement need** not be the same as the distance moved.

## How Is Displacement Defined

As this is a calculation that measures distance, its standard unit is the meter . For many applications in Physics concept of displacement is very useful. Displacement is the difference between two positions of an object. It is a vector quantity because it has a direction and magnitude as well. It is represented as an arrow that points from the starting position to the last position.

For Example, if an object moves from the first position to the last position, then the objects position changes. This change in the position of an object is referred to as displacement.

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## Displacement And Distance Problems With Solutions

Problems and Solutions about distance and displacement are presented and updated useful for high school and college students.

In the following, displacement is computed for simple cases,

**Problem : **

**An object moves from point A to B, C, and D finally, along a rectangle. Find the magnitude and direction of the displacement vector of the object? Find the distance traveled by that object? Suppose the object returns to point A, its initial position. Now, Find the displacement and distance?**

**Solution :**

distance is equal to the length of AB+BC+CD. Since the initial and final positions are the same, so by definition of displacement, the difference between them is zero. But distance, in this case, is the perimeter of the rectangle.

It is also possible to find the displacement of a moving object along a straight line using a position vs. time graph.

**Problem 2:**

**An object moves along a right triangle from point A to B to C shown in the figure below. Find the magnitude and direction of the displacement vector? How much distance is traveled by this moving object? Suppose the object returns to point A, its initial position. Now, Find the displacement and distance?**

Adding the base and height of this triangle gets the distance traveled from to .\begin \text & = a + b\\ & = 3 + 4\\ & = 7\, \end

Displacement is zero since the object returns to the initial position. Distance is also computed as the perimeter of the triangle.

## Magnitude And Direction Of Resultant Displacement

*check_circle*

Magnitude of displacement will be 134.16 m and direction will be 45

First displacement of 30 due south and then 30 m due east.

**Formula Used:**

The resultant of two vectors is given by,

Here, P and Q are two vectors which are perpendicular to each other.

**Calculation:**

It is given first displacement is 30 m due south.

And then 30 m due east.

Let 30 m

From the vector principle when two vectors are perpendicular to each other then their resultant magnitude is given by,

Magnitude of displacement by graphical method is shown below.

It is given first displacement is 30 m due south.

Therefore,

Then 30 m due east.

Therefore,

So the resultant displacement will be,

Now direction of displacement will be,

Therefore direction of displacement will be 45

As the magnitude of displacement is same by both mathematical and by graphical method.

Therefore, magnitude of displacement will be 134.16 m and direction will be 45

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## What Is Magnitude In Physics

In Physics, magnitude is defined as the maximum extent of size and the direction of an object. Magnitude is used as a common factor in vector and scalar quantities. By definition, we know that scalar quantities are those quantities that have magnitude only. Whereas vector quantities are those quantities that have both magnitude and direction.

There are different ways in which magnitude can be used. Some of them are:

- Magnitude of earthquake
- Magnitude of charge on an electron
- Magnitude of force
- Magnitude of gravitational force

## What Is The Magnitude Of The Final Displacement

The magnitude of the displacement is always positive. This is the absolute value of the displacement, because displacement is a vector and cannot have a negative value of magnitude. In our example, the magnitude of the total displacement is 2 m, whereas the magnitudes of the individual displacements are 2 m and 4 m.

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## Magnitude Of Charge On An Electron

The charge of an electron is the same as that of the magnitude of the elementary charge, e with a negative sign. The value of the elementary charge is 1.602 x 10-19 C.

We know that there are two types of electric charges, and they are positive and negative. The positively charged are known as protons while the negatively charged are known as electrons. The net charge of an object is said to be positive if there are more protons than electrons. Likewise, the net charge of an object is said to be negative if there are more electrons than protons. However, if the number of protons and electrons are equal, then the object is said to be electrically neutral.

## Solution For Problem 40 Chapter 3

Physics | 4th Edition

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Physics | 4th Edition

What are the direction and magnitude of your total displacement if you have traveled due west with a speed of 27 m/s for 125 s, then due south at 14 m/s for 66 s?

Q: What are the direction and magnitude of your total displacement if you have traveled due west with a speed of 27 m/s for 125 s, then due south at 14 m/s for 66 s?

Step By Step Solution

##### ISBN: 9780321611116

Physics was written by and is associated to the ISBN: 9780321611116. This textbook survival guide was created for the textbook: Physics, edition: 4. The full step-by-step solution to problem: 40 from chapter: 3 was answered by , our top Physics solution expert on 11/15/17, 04:23PM. This full solution covers the following key subjects: due, South, direction, magnitude, displacement. This expansive textbook survival guide covers 32 chapters, and 3407 solutions. Since the solution to 40 from 3 chapter was answered, more than 530 students have viewed the full step-by-step answer. The answer to What are the direction and magnitude of your total displacement if you have traveled due west with a speed of 27 m/s for 125 s, then due south at 14 m/s for 66 s? is broken down into a number of easy to follow steps, and 34 words.

#### Other solutions

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## The Formula Of Displacement

The official displacement formula is as follows:

\ | final position |

Displacements are not necessarily always positive. It can be zero or negative as well. If the positive direction is to the right of the origin, then a negative displacement means that the object has moved towards the left of the origin.

In Physics problems, we can choose to place the origin of our position-measuring system wherever is convenient. The measurement of the position of an object depends on where we choose to place the origin.

The displacement from an initial position s_i to a final position s_f does not depend on the position of the origin. This is because the displacement depends only on the difference between the two positions, and not the positions themselves.

Distance and displacement are two quantities that are similar. But these are having some differences also.

- Distance is a scalar quantity that refers to how much ground an object has covered during the motion.
- Displacement is a vector quantity which refers to how far out of place an object is, it is the objects overall change in the position.

## What Is Magnitude In Physics In The Case Of Earthquakes

A tremendous amount of energy is released during an earthquake and results in the formation of seismic waves.

These waves travel in all directions, causing destructive vibrations.

The magnitude of an earthquake provides the necessary information, which can help calculate the probabilities in time to come.

Magnitude is the quantitative value for seismic waves formed by an earthquake.

The scale that measures earthquakes is called a Richter scale.

It is a logarithmic scale in which the magnitude increases ten times with each increase in the number.

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