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# Kinematic Equations Calculator + Online Solver With Free Steps

The **Kinematic Equations Calculator** is used to compute the **time** and **distance** covered by a body using the equations of motion. It takes the **initial velocity**, **final velocity**, and **acceleration** of the body as input and outputs the remaining parameters in the Kinematic Equations.

**Kinematics** is the branch of physics that deals with object translational and rotational motion. It is mainly a branch of **mechanics** that ignores all the physical properties and **forces** acting on the body and considers the motion.

**Motion** is defined as the **movement** of an object concerning some **reference point**—the position of the body changes when in motion. **Distance** is defined as how much** path** the body has covered in some time t. It is directly proportional to the **speed** of the body. **Velocity** is defined as the rate of change of displacement. It has both a magnitude and a direction, so it is a **vector** quantity. The mathematical **formula** for velocity can be written as:

\[ v = \frac{ \Delta d }{ \Delta t } \]

**Acceleration** is the time rate of change of velocity. It tells how much the speed of the moving body varies with time. It is also a **vector** quantity.

If the body moves with **constant velocity**, it has **zero acceleration**. Acceleration can be defined mathematically as:

\[ a = \frac{ \Delta v }{ \Delta t } \]

## What Is a Kinematic Equations Calculator?

**The Kinematic Equations Calculator is an online tool that is used to calculate the time t the body took to change its velocity and the distance D traveled by the body using the Kinematic Equations.**

There are **three** Kinematic Equations or equations of motion. They are linear equations that describe the **translational motion** of a body. It means that the body is moving in a straight line.

Consider a body moving in a **straight path** with initial velocity** $v_1$**. After some time **t**, the body covers a distance** D**, and its velocity changes to **$v_2$** with a uniform acceleration** a**.

The **three Kinematic Equations** for this moving body are as follows:

\[ v_{2} = v_{1} + at \]

\[ D = v_{1} t + \frac{1}{2} a t^{2} \]

\[ 2aD = {v_{2}}^2 \ – \ {v_{1}}^2 \]

These equations play an essential role in **mechanics** while dealing with translational motion.

## How To Use the Kinematic Equations Calculator

The user can use the **Kinematic Equations Calculator** by following the steps given below.

### Step 1

The user must first enter the acceleration with which the body is moving. It should be entered in the block against the title; “**Acceleration**” in the calculator’s input window.

The acceleration should be in the units of **meters per second squared** (m/s.s).

### Step 2

The user must now enter the initial velocity in the input tab of the calculator. Initial velocity is the velocity with which the body starts moving.

It should be entered in the block labeled; “**Initial Velocity**.” The unit for velocity should be **meters per second** (m/s).

### Step 3

The user must now enter the final velocity, which becomes the body’s velocity after some time t. It should be entered in the “**Final Velocity**” block as the input data.

This change in the velocity from initial to final produces a **uniform acceleration** after covering some distance in some elapsed time.

### Step 4

The user must now press the “**Submit**” button after the required **parameters** of the **Kinematic Equations** are entered in the calculator’s input window.

The calculator processes the input data and computes the **output** using motion equations.

### Output

The calculator displays the output in the following **three windows** as given below.

#### Input Interpretation

The calculator interprets the **input data** and shows it in this window. This helps the user to **reassure** the input values and to correct them if needed.

It shows the initial velocity, final velocity, and acceleration values as entered by the user.

#### Distance

The calculator computes the **distance** by using the **third equation** of motion. It is given as follows:

\[ 2aD = {v_{2}}^2 \ – \ {v_{1}}^2 \]

Dividing by **2a** gives the displacement **D** as:

\[ D = \frac{ {v_{2}}^2 \ – \ {v_{1}}^2 }{ 2a } \]

Putting the values of initial velocity **$v_1$**, final velocity **$v_2$**, and acceleration **a** gives the distance **D**.

#### Time

The time the body takes to **change its velocity** is calculated using the first equation of motion. The calculator uses the **first equation** of motion as follows:

\[ v_{2} = v_{1} + at \]

Subtracting “**at**” on both sides gives:

\[ v_{2} \ – \ at = v_{1} \]

The equation can be rewritten as:

\[ v_{2} \ – \ v_{1} = at \]

Dividing by “**a**” on both sides gives the time “**t**” as follows:

\[ t = \frac{ v_{2} \ – \ v_{1} }{a} \]

The calculator uses this modified form of the equation to calculate the **time**.

## Solved Examples

The following examples are solved through the **Kinematics Equations Calculator**.

### Example 1

A body is moving with an initial velocity of **10 m/s**. It changes its velocity to **50 m/s,** accelerating at **20 m/s$^2$**. Calculate the **distance** covered and the **time** taken by the body to change its velocity.

### Solution

The user must first enter the acceleration, initial velocity, and final velocity in the** input** window of the calculator. They should be entered as follows:

**Acceleration = 20 m/s.s**

**Initial Velocity = 10 m/s**

**Final Velocity = 50 m/s**

The calculator computes the **distance D** as **60 m** and the **time t** as **2 sec**.

### Example 2

Given:

**Acceleration = 35 m/s.s**

**Initial Velocity = 7 m/s**

**Final Velocity = 21 m/s**

Calculate the **distance** traveled and the** time** taken to change the body’s velocity.

### Solution

The user must first enter the **three parameters** of the Kinematics equation in the calculator’s input tab as given in this example.

After pressing “**Submit,”** the calculator shows the result as follows:

**Distance = 5.6 meters**

**Time = 0.4 seconds**