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# Kinematics Calculator + Online Solver With Free Steps

The **Kinematics Calculator** is an advanced online tool to calculate parameters related to the motion of an object. To perform computations, the calculator requires three elements: initial velocity, final velocity, and acceleration of the object.

The **calculator** using these elements provides values of distance and time taken by the object to perform the motion. Hence, it is a beneficial and powerful tool for students, mechanical engineers, and physics researchers.

## What Is the Kinematics Calculator?

**The Kinematics Calculator is an online tool that can find the distance covered and the time a moving object takes based on its velocity and acceleration.**

**Kinematics** is an analytical study of objects that performs any kind of motion. It is widely used in areas of **physics** and **mechanics**. For example, the distance traveled by car or the flight time of a missile.

Specific mathematical formulas are used for these kinematics parameters. Therefore you must remember them and have good knowledge of kinematics.

But you can resolve problems effortlessly with the quick and easy-to-use **Kinematics Calculator**. It achieves state-of-the-art performance by giving the most accurate and precise results.

## How To Use the Kinematics Calculator?

To use the **Kinematics Calculator,** we plug in the three required parameters in their respective fields. The calculator performs the calculations assuming the acceleration of the object remains constant.

The step-by-step procedure for using the calculator can be seen below:

### Step 1

In the first field, insert the **acceleration** of the object. The acceleration should be in the standard unit, $m/s^{2}$.

### Step 2

Enter the **initial velocity** of the object in the second field.

### Step 3

Then put the value of the **final velocity** in the last input field. Both of the speeds should also be in their standard unit, **m/s**.

### Step 4

After entering all the values, use the ‘**Submit**’ button to acquire the results.

### Result

The result of the calculator contains values of two quantities. The first one is the **time** the object takes to reach the provided final velocity. The second quantity is the **distance** the thing travels while reaching the point of final velocity.

## How Does the Kinematics Calculator Work?

The kinematics calculator works by finding the **distance **traveled and** time **taken with the help of the given acceleration, initial velocity, and final velocity inputs through the **kinematic equations**.

This calculator solves the problems involving the kinematic equations, but there should be good knowledge about kinematics and its equations before solving the problems.

### What Is Kinematics?

Kinematics is a branch of physics and classical mechanics that studies the geometrically possible** motion** of a body without taking into account the forces involved. It describes the motion of an object by trajectories of points, lines, and other geometric entities.

Kinematics also focuses on differential quantities that are **velocity** and **acceleration**. It displays the spatial position of bodies. It is commonly used in mechanical engineering, robotics, astrophysics, and biomechanics.

The motion interpretation in kinematics is feasible only for objects with constrained motions because the causative forces are not considered. The study of kinematics consists of three concepts: position, velocity, and acceleration.

#### Position

The position describes the** location** of an object. It is denoted by the variables such as ‘x,’ ‘y’, ‘z,’ ‘d’, or ‘p’ in numerical problems of physics. The** change** in the position of a body is known as** displacement, **which is represented by $ \Delta$x, $ \Delta$y.

Position and displacement are both measured in meters.

#### Velocity

Velocity is the change in** displacement** over time. It tells how fast a body is moving and shows its direction also. It is displayed by a variable ‘**v**’ and measured in meters per second or ‘**m/s**.’

The constant velocity can be found by the change in position divided by the change in the time given by the equation ‘**v= $ \Delta$x/$ \Delta$t**’.

#### Acceleration

The rate of change in the **velocity **is called acceleration. If the object speeds up or slows down while moving in a straight path, then the object is **accelerated**. If the speed is constant, but the direction is continuously changing, then the acceleration is also there.

It is represented using the letter ‘**a**’, and the measuring unit is the meter per second squared or **‘m/$s^2$**’. The equation used to calculate the acceleration when it is constant is given by **a= $ \Delta$v/$ \Delta$t**.

### Kinematics Equations

Kinematics equations consist of** four **equations used to determine the unknown quantity related to an object’s motion with the help of known quantities.

These equations depict the motion of a body at either** constant acceleration** or **constant velocity**. They can not be applied over that interval during which each of the two quantities changes.

Kinematic equations define the relation among **five** kinematic variables: displacement, initial velocity, final velocity, time interval, and constant acceleration.

Therefore if the value of at least three variables is given, the other two variables can be found.

The four kinematic equations are given below:

- \[v_f = v_i + a*t\]
- \[s = v_i*t +(1/2) a*t^2\]
- \[v_f^2 = v_i^2 + 2*a*s\]
- \[s = \frac{(v_i + v_f)}{2}*t\]

This calculator accepts the three kinematic variables: constant** acceleration**, **initial velocity**, and** final velocity. As** a result, it provides the calculated** distance **traveled and the** time **with the help of above mentioned kinematic equations.

## Solved Examples

For a better understanding of the operation of the calculator, the following problems are solved.

### Example 1

A racing car starts with rest and achieves a final velocity of **110 m/s**. The car has a uniform acceleration of **25 $m/s^{2}$**. Calculate the total time taken and the distance the car covers to achieve the final velocity.

### Solution

The solution to this problem can be obtained easily using the **Kinematics Calculator**.

#### Distance

The distance covered by the racing car is given below:

**Distance** (d) = **242** meters

#### Time

The time taken by the racing car to achieve the final velocity is as follows:

**Time **(t) =** 4.4 **sec

### Example 2

Consider a pilot who reduces his plane speed from **260 m/s** to the rest with the deceleration of **35 $m/s^{2}$ **for landing. How much time and part of the runway will it take to stop the plane?

### Solution

The calculator gives the following solution.

#### Distance

The deceleration is taken as negative acceleration in this problem as the plane’s speed is reduced.

**Distance** (d) = **965.71** meters

It will take 966 meters of runway to stop the plane properly.

#### Time

The plane will be stopped in approximately 8 seconds.

**Time **(t) =** 7.4286 **sec