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Physics Calculators ▶ Kinematics Calculator

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This kinematics calculator will help you solve the uniform acceleration problems by using kinematics equations of physics. You can use our free kinematic equations solver to solve the equations that is used for motion in a straight line with constant acceleration.

Kinematics is referred to as a subfield of physics that developed in classical mechanics. In physics, it represents the motion of points, bodies, as well as the system of bodies without considering the forces, which cause them to move. More specifically, kinematics indicated as the study of the objects in motion, there velocity, acceleration and momentum.

Example: Train moving, Flowing water in a river.

It doesn’t matter whether you are dealing with the motion of points, or an object, this kinematics calculator helps you to determine the kinematics.

The kinematic formulas are referred to as a set of formulas that use the five kinematic variables given below:

\(s\) = Displacement

\(t\) = Time taken

\(u\) = Initial velocity

\(v\) = Final velocity

\(a\) = Constant acceleration

If you know any three of these five kinematic variables \((s, t, u, v, a)\) for an object under constant acceleration, then you can use a kinematic formula.

Typically, the kinematic formulas are written as the given four equations. Even our kinematic equations calculator uses the following four equations to find the unknown variables:

$$ v = u + at $$

$$ s = ut + \frac {1}{2}at^2 $$

$$ v^2 = u^2 + 2as $$

$$ s = (\frac {v + u}{2}) t $$

Remember that these formulas are only accurate if the acceleration is constant during the time taken considered, so, you should be careful not to use them when the acceleration is changing. Also, the variables of the kinematic equations are referring to the same direction: horizontal x, vertical y.

For ease, you can also use our online acceleration calculator for the calculations of the acceleration of the moving object from the different calculation formulas.

The calculations for the moving object become very easy with this tool. Here we have some manual examples. After reading, you will be able to completely solve different kinematics equations:

Read on!

**Example 1:**

An object start with the velocity of \(2ms^{-1}\) , after \(8\) seconds attain the velocity of \(30ms^{-1}\). Determine the acceleration and the distance covered by the object?

**Solution:**

Here,

\(u = 2 ms^{-1}\)

\(v = 30 ms^{-1}\)

\(t = 8s\)

So,

By first equation of motion:

\(v = u + at\)

\(30 = 2 + a(8)\)

\(30-2 = 8a\)

\(28 = 8a\)

\(a = 28/8\)

\(a = 3.5ms^{-12}\)

Now, using second equation of motion:

\(S = ut + Â½ at^{2}\)

\(S = (2)(8) + Â½ (3.5)(8)^{2}\)

\(S = 16 + Â½ (3.5)(64)\)

\(S = 16 + Â½ (224)\)

\(S = 16 +112\)

\(S = 128m\)

**Example 2:**

A body moves with an acceleration of \(4ms^{-2}\) in \(14 s\) and covers a displacement of \(40 m\). Find the initial & final velocity of the body?

**Solution:**

Here,

\(a = 4ms^{-2}\)

\(t = 14s\)

\(S = 40m\)

From the second equation of motion:

\(S = ut + Â½ at^{2}\)

\(u = S – Â½ at^{2} / t \)

\(u = 40 – Â½ (4)(14)^{2}/ 14\)

\(u = 40 – Â½ (4)(196) / 14\)

\(u = 40 â€“ (0.5) (4)(196) / 14\)

\(u = 40 â€“ 392 / 14\)

\(u =â€“ 352 / 14\)

\(u = -25.14ms^{-1}\)

Now, using first equation:

\(v = u + at\)

\(v = -25.14 + 4*14\)

\(v = -25.14 + 56\)

\(v = 30.85ms^{-1}\)

No doubt, it is very hard to remember these formulas for kinematics, but, thanks to the kinematic equations calculator that helps you to solve equations of motion problems accurtaely.

Follow the below-mentioned steps to use this kinematics solver.

**Inputs:**

- First of all, choose which two variables you want to find from the dropdown menu.
- Then, enter the data in all the fields according to the selected option.
- Lastly hit the calculate button.

**Outputs:**

Once you fill all the fields, the calculator shows:

- Initial Velocity.
- Final Velocity.
- Displacement
- Acceleration
- Time
- Formulas that are used.

**Note:**

No matter, whatâ€™s your input is, the kinematics calculator shows you the results according to your selected kinematic equations.

The acceleration is the rate of change of velocity of a moving object. Simply, dividing the velocity with the time taken by an object gives the acceleration of the object.

Kinematic variables including position, velocity & acceleration of the body can be used to describe the state of rest or motion of the body. They are used in many real-life fields like mechanical engineering, biomechanics, and robotics to describe the motion of the engine, the skeleton of the human body, or the robot. So, to solve the kinematics formulas for any of the variables, you can try this online kinematics calculator that helps you to do the calculations for the state of the moving object accurately.

From the source of Wikipedia : General overview of Kinematics

From the site of Khanacademy : Kinematic formulas & Equation of motion

From the source of physicsclassroom : How to use the kinematic equations