## Displacement Definition: What Is Displacement

Let’s start from the beginning with the displacement definition. Displacement means different things in different contexts, so what is displacement in physics? In physics , displacement is the amount an object has moved **regardless of the path taken**.

We will see this better when we look at the displacement formula, but displacement can be thought of as the distance between the starting point and the finishing point. It doesn’t take into account the path taken to get from one point to the other, so it doesn’t measure the distance traveled.

The distance between cities, for example, from New York to Washington, you have to travel depends on the route you take. However, no matter what road you choose, the final displacement will always be the same: the straight-line distance from one city to the other.

Did you know that another type of displacement is known as angular displacement! If you want to know more about it, check out our angular displacement calculator.

## Similarities Between Distance And Displacement

Despite a number of differences between them, both distance and displacement have quite similarities as well, some of them are listed below:

- The SI unit of both the Physical quantity is meter only.
- Both distance and displacement require initial and final points for measurement.
- When the direction is not considered both are equal in magnitude, in most cases.
- Both have the same dimensions formula.

## Displacement Formulas How To Calculate Displacement

We find the displacement by determining the objects initial and final position. The displacement formula is given by:

x = xf xi..

xf is the final position,

xi is the initial position, and

x is the change in the position of the object.

Lets say, I kept a golf ball on the origin or the 0 points, as shown in diagram A:

Now, I move the ball by 3 points to the right, as shown in diagram B.

Since the ball has moved, which means it has made a displacement, as we can see its initial position was 0 at A and the final is 3 metres at point B, so its displacement can be calculated by using equation 1, which is:

x = xf xi= 3 0 = + 3 m, i.e., to the right.

So, the ball made a displacement of 3 meters from A to B.

Now, the ball moves by 4 points or 4 m to point C.

So, the final position now becomes an initial one and final, xi= 4 m. So, we can find the displacement AC by using eq as:

x = xf xi= 4 = 7 m, i.e., to the left.

However, we must remember that displacement doesnt depend on the position of the origin, as we saw in the diagram, it only depends on the difference between the two positions.

Here,

x1 = x-coordinate of point A, i.e., the initial position of an object along the x-axis

x2 = x-coordinate of point B, i.e., the final position of an object along the x-axis

The horizontal distance, i.e., along the x-axis =

y1 = y-coordinate of point A, i.e., the initial position of an object along the y-axis

The vertical distance, i.e., along the y-axis =

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## 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.

## Solved Examples On Distance And Displacement

**Example 1: What is the distance and displacement from the given figure,**

**Solution:**

Distance is the total path length,

Distance = m = 7meters.

Displacement is the direct line from A to B,

Displacement=

Therefore, Displacement= 5 meters .

**Example 2: A particle has covered a distance of 1000 meters and a displacement of 200 meters in 1 min 40 sec. Find the Speed and Velocity of the particle during motion.**

**Solution:**

Distance gives detailed info about path length Displacement does not give detailed information about the path length.

**Question 2: Is this possible to have a negative distance?**

**Answer:**

No, distance can never be negative. Distance is always positive. However, displacement can be negative.

**Question 3: Can displacement be zero?**

**Answer:**

Yes, displacement can be zero.

**Question 4: When do the Distance and Magnitude of Displacement become equal?**

**Answer:**

The distance and the magnitude become equal when the motion is in a fixed direction or in one direction.

**Question 5: Write any two differences between distance and displacement.**

**Answer:**

Distance is a scalar quantity while displacement is a vector quantity.

Also, Displacement can be positive, negative or zero but Distance can only be positive.

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## Difference Between Distance And Displacement

Here are the tabular representation of the differences between Distance and Displacement:

Distance |
Displacement |
---|---|

Distance is the total path covered by the object in motion, irrespective of the direction of the path. | Displacement is defined as the total change in the position of the object along with the direction of motion. |

Distance is denoted by the symbol d. |
Displacement is represented by the letter s. |

Distance is a Scalar Quantity. |
Displacement is a Vector Quantity. |

When Distance is calculated, only the length of the path is considered, ignoring its direction. | When Displacement is calculated, both the length of the path and the direction of the object are considered. |

The formula to calculate the distance is equal to Speed × time. | The formula to calculate the Displacement is equal to Velocity × time. |

The distance can only have positive values. | However, displacement can have positive, negative, or zero. |

## Solved Example On Displacement Formula

**Example 1**

Suppose Radha leaves Mumbai to visit Meena in Delhi. Also, she traveled through the train and first of all, she travels 350 kilometers to the north. But, then the track turns back to south 125 kilometers. Calculate Radhas total displacement using displacement formula?

**Solution:**

The initial position of Radha is \ = 0 and her final position \ is the distance she traveled towards north minus the distance she traveled towards the south. So, now put the values in the equations

D = \ = \D = D = 225 km N

So the total displacement of Radha is 225 kilometer towards the north.

**Example 2**

Suppose you throw a ball 25 feet north of your dog and ordered him to fetch the ball. After picking up the ball he takes it past you to your brother, who is standing 5 feet south to you from where you are standing. So, find the displacement of the ball?

**Solution:**

The initial position of the ball is \ = 0 feet. Moreover, displacement is a vector quantity and direction is considered. \ = , So the \ = 5 feet south.

Putting values in the formula

D = \ = \D = D = 5 ft

The displacement of the ball is 5 ft south of the initial position.

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## Examples Of Distance And Displacement

**Question 1. John travels 250 miles to North but then back-tracks to South for 105 miles to pick up a friend. What is Johns total displacement?**

**Answer: **Johns starting position Xi= 0.

Her final position Xf is the distance travelled N minus the distance South.

Calculating displacement, i.e.D.

D = 0

D = 145 mi N

**Question 2. An object moves along the grid through points A, B, C, D, E, and F as shown below. The side of square tiles measures 0.5 km.**

**a) Calculate the distance covered by the moving object.**

**b) Find the magnitude of the displacement of the object.**

**Solution:**

a) The distance covered by the moving object is calculated as follows:

AB + BC + CD + DE + EF

3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km

The distance covered by the moving object is 6.5 km.

b) The initial point is A and the final point is F, hence the magnitude of the displacement is equal to the distance AF which is calculated by applying Pythagorass theorem to the triangle AHF as shown in the figure below

Applying the Pythagorean formula, we get

Substituting the formula, we get

The magnitude of displacement is 2.5 km.

## How To Find Displacement In Physics

In this article learn about how to find displacement in physics. Here we will learn about **Displacement formulas** and how to use them to find displacement in physics.

Many people use the terms distance and displacement interchangeably. But in reality, both distance and displacement are two different concepts.

*Displacement is defined as a change in the position of an object. Now when an object is displaced it covers a distance in a particular direction.*

Since it has both magnitude and direction displacement is a vector quantity. For more clarity consider an object moving from point A to point B.

Here the object under consideration moves through this red line path. Here this red lines path gives the total distance covered by the object moving from point A to point B.

But the green line points from point A to point B in the shortest possible distance between these two points with its direction pointing from initial point A to final point B. This shortest distance from point A to point B is nothing but a **displacement of the object**.

Now as such we have two cases of formulas for finding displacement in kinematics.

- The first one is where only the position of the object is given that is we have information about the initial and final positions of the object in motion.
- In our second case, we use kinematics equations that involve distance along with other parameters like velocity, acceleration, and time.

Let us now look at how to find displacement in physics.

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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 The Displacement Formula

As previously stated, displacement is the vector going from an initial position \ to a final position \. Therefore, the equation to calculate the displacement \ looks like this:

It is important to know that when it comes to displacement, the value can be negative depending on the direction of the displacement. If we choose upwards to be positive, then the displacement of a skydiver between jumping and landing is negative. However, if we choose upwards to be negative, then their displacement is positive! Meanwhile, the distance between their jumping and landing will be positive in both cases.

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## How Do You Find Displacement With Angle And Distance

Angular displacement seeks to measure the shortest distance between the initial location and final location when an object isnt moving in a straight line. The formula for angular displacement is: = S/r, where S stands for linear displacement, r stands for radius, and represents angular displacement.

## Formula For Calculating Displacement In Physics

**The formula for displacement can be:**

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## Displacement Calculations Used In Calculator:

Solving for the different variables we can use the following formulas:

- Given u, t and a calculate s Given initial velocity, time and acceleration calculate the displacement.
- s = ut + ½at2: solve for s

## How To Calculate Displacement

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Displacement in physics refers to on object’s change in position. When you calculate displacement, you measure how “out of place” on object is based on its initial location and its final location. The formula you use for calculating displacement will depend on variables that are provided to you in a given problem. Follow these steps to calculate displacement.

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## 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.

## Solved Examples On Displacement Formula

Question 1: Find the displacement covered by an object which accelerates from rest to 60 m/s in 3s.

Solution: Initial velocity = 0 and final velocity = 60 m/s.

Time taken = 3s.

Displacement = ut + ½ at2

= 90 m

Question 2: Find the displacement of an object if it moves with an acceleration of 4 m/s2 for 5s, where the initial velocity was 2 m/s.

Solution: Given initial velocity = 2 m/s, acceleration a = 4 m/s2 , and t = 5s, so the displacement will be:

Displacement =\

Also, we know that

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## How To Find The Magnitude Of Displacement

Now the questions discussed below will teach you how to find the magnitude of displacement.

Question 2 The path distance from the playground to a school is 9 m west and then 4 m south. A builder wants to build a short-distance path for it. Find the displacement length of the shortest path.

Solution. It is given in the question that

Distance to the west $x = 9 m$

Distance to the south $y = 4 m$

Displacement is given by

$d=\sqrt$

$d=\sqrt = 9.85m$

So, the builder can build a path length of 9.85 m from the playground to the school.

**Question 3.** An object moves through a distance of 3 miles due east and then 4 miles due north.

**Solution.** The situation described in the question is shown below in the figure. This problem uses the resultant displacement formula for finding the displacement of the object.

The object starts from O. It moves through a distance of 3 miles due east to reach A and then through a distance of 4 miles due north to reach B.

## How To Calculate Displacement: Displacement Formula

So, how to calculate displacement if it isn’t the same as the distance traveled? The first thing to do is look at the displacement formula and forget about the displacement vs. distance debates. There are many formulations of the displacement formula, but the one we are interested in is this:

- t is the time taken from start to finish and

Alternatively, we could calculate the average velocity from a collection of velocities by doing a weighted average of them, where the weight of each velocity is the time spent at that velocity. You can do it conveniently using the weighted average calculator.

If you want to know how to find the average rate of change of distance with time , check the average rate of change calculator.

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