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# Displacement Calculator

Choose the quantity, fill the required input boxes, and press calculate button using displacement calculator

Table of Contents:

## Displacement Calculator

Displacement calculator is used to evaluate the displacement of an object using the time taken in its movements, and the initial & final velocity of the body in its movements.

## What is the displacement?

**Displacement **tells us the position or total distance covered by the object with respect to the initial position and final position. It is the distance traveled by an object between its starting and finishing points that is the shortest.

Moreover, displacement is a **vector quantity** that includes the magnitude and direction. Its SI unit is a **meter **represented by the symbol “**m**”.

### Formula:

- The mathematical formula of displacement is stated as.

**S = 1/2(v _{f }+ v_{i}) × t**

- To find the
**time**of the object the formula becomes.

**t = 2S/v _{f} + v_{i}**

- To find the
**final velocity**of the object the formula becomes.

**v _{f} = 2(S/t )- v_{i}**

- To find the
**initial velocity**of the object the formula becomes.

**v _{i} = 2(S/t) - v_{f}**

Where,

**S**= displacement of the object with respect to the position**v**= object final velocity_{f }**v**= object initial velocity_{i}**t**= time taken for the object to undergo displacement.

## How to find the displacement?

**Example 1:**

Evaluate the displacement of the object if the object moves with an initial velocity of **10 m/s** in **20 seconds** and finally comes in to rest with the speed of **30 m/s **at the end.

**Solution:**

**Step 1:**

**Write the data carefully from the above question.**

S = displacement with respect to position =?, v_{f }= final velocity = 30

v_{i} = initial velocity = 10, t = time taken = 20

**Step 2: **

**Write the formula of the displacement in detail.**

`S = 1/2(v`

_{f }+ v_{i}) × t

**Step 3:**

**Put all values in the above formula and simplify carefully.**

v_{f} = 30, v_{i} = 10, t = 20

S = 1/2(v_{f }+ v_{i}) × t

S = 1/2(30 + 10) × 20

S = 1/2(40) × 20

S = 20 × 20

**S = 400 m**

**Example 2:**

Evaluate the initial velocity of the object if the object covers **100 meters** in **2 seconds** and finally comes in to rest with the speed of **40 m/s** at the end.

**Solution:**

**Step 1:**

**Write the data carefully from the above question.**

S = displacement with respect to position =100, v_{f }= final velocity = 40

v_{i} = initial velocity = ?, t = time taken = 2

**Step 2: **

**Write the formula of the initial velocity in detail.**

`v`

_{i} = 2(S/t) - v_{f}

**Step 3:**

**Put all values in the above formula and simplify carefully.**

S = 100, v_{f} = 40, t = 2

v_{i} = 2(S/t) - v_{f}

v_{i} = 2(100/2) - 40

v_{i} = 2(50) – 40

v_{i} = 100 - 40

`v`

_{i}** = 60 m/s**

**Example 3:**

Evaluate the final velocity of the object if the object covers **600m** in **20 seconds** and its initial velocity is **10 m/s**.

**Solution:**

**Step 1:**

**Write the data carefully from the above question.**

S = displacement with respect to position = 600, v_{f }= final velocity = ?

v_{i} = initial velocity = 10, t = time taken = 20

**Step 2: **

**Write the formula of the initial velocity in detail.**

`v`

_{f} = 2(S/t )- v_{i}

**Step 3:**

**Put all values in the above formula and simplify carefully.**

S = 600, v_{i} = 10, t = 2o

v_{f} = 2(S/t )- v_{i}

v_{f} = 2(600/20) - 10

v_{f} = 2(30) – 10

v_{f} = 60 - 10

**v _{f} = 50 m/s**