Kinematics Calculator

Kinematics Calculator

Select the parameters and write the required ones against them. The calculator will readily calculate results by employing kinematics equations.

Find:

Initial Velocity ( u )

m/s ▾

Final Velocity ( v )

m/s ▾

Time ( t )

sec ▾

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.

What is Kinematics?

Kinematics is a subfield of physics that developed within classical mechanics. It deals with the motion of points, bodies, and systems of bodies without considering the forces that cause the motion. More specifically, kinematics is the study of objects in motion, including their velocity, acceleration, and displacement. Examples include a moving train or flowing water in a river. Whether you are analyzing the motion of a point or an entire object, this kinematics calculator helps you determine the relevant kinematic variables.

What are Kinematics Formulas?

Kinematic formulas are a set of equations that relate five key kinematic variables:

$s$ = Displacement

$t$ = Time taken

$u$ = Initial velocity

$v$ = Final velocity

$a$ = Constant acceleration

If you know any three of these five variables $(s, t, u, v, a)$ for an object under constant acceleration, you can use a kinematic formula to find the unknowns. The four commonly used kinematic equations are:

$$ v = u + at $$

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

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

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

These formulas are valid only when the acceleration is constant during the time interval considered. Ensure all variables refer to the same direction (horizontal x or vertical y). For convenience, you can also use our online acceleration calculator to compute acceleration from different kinematic relationships.

Manual Examples Where You Can Use the Kinematics Calculator:

Using this tool makes calculations for moving objects simple and accurate. Here are some manual examples to help you understand how to solve various kinematics equations effectively. Read on to learn more!

Example 1:

An object starts with a velocity of $2 \, \text{m/s}$. After 8 seconds, it attains a velocity of $30 \, \text{m/s}$. Determine the acceleration and the distance covered by the object.

Solution:

Given:

$u = 2 \, \text{m/s}$

$v = 30 \, \text{m/s}$

$t = 8 \, \text{s}$

Using the first equation of motion:

$v = u + at$

$30 = 2 + a(8)$

$30 - 2 = 8a$

$28 = 8a$

$a = \frac{28}{8} = 3.5 \, \text{m/s}^2$

Using the second equation of motion to find displacement:

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

$S = (2)(8) + \frac{1}{2}(3.5)(8)^2$

$S = 16 + \frac{1}{2}(3.5)(64)$

$S = 16 + 112$

$S = 128 \, \text{m}$

Example 2:

A body moves with an acceleration of $4 \, \text{m/s}^2$ for 14 seconds and covers a displacement of 40 m. Find the initial and final velocity of the body.

Solution:

Given:

$a = 4 \, \text{m/s}^2$

$t = 14 \, \text{s}$

$S = 40 \, \text{m}$

From the second equation of motion:

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

$u = \frac{S - \frac{1}{2}at^2}{t}$

$u = \frac{40 - \frac{1}{2}(4)(14)^2}{14}$

$u = \frac{40 - (2)(196)}{14}$

$u = \frac{40 - 392}{14}$

$u = \frac{-352}{14} \approx -25.14 \, \text{m/s}$

Using the first equation to find final velocity:

$v = u + at$

$v = -25.14 + 4 \cdot 14$

$v = -25.14 + 56$

$v \approx 30.86 \, \text{m/s}$

Remembering kinematic formulas can be challenging, but with a kinematic equations calculator, you can solve motion problems accurately and quickly.

How to Use This Online Kinematics Calculator?

Follow these simple steps to use the kinematics solver:

Inputs:

First, choose which variable you want to find from the dropdown menu.
Enter the known values in all the fields according to the selected option.
Click the "Calculate" button to get the results.

Outputs: Once all fields are filled, the calculator shows:

Initial Velocity
Final Velocity
Displacement
Acceleration
Time
The formulas that were used for the calculation

Note: Regardless of the input, the kinematics calculator provides results based on the selected kinematic equations.

Frequently Asked Questions (FAQ’s):

How do I Find Average Acceleration in Kinematics?

Acceleration is the rate of change of velocity of a moving object. Simply divide the change in velocity by the time taken to get the average acceleration of the object.

Is Time a Kinematic Variable?

Yes, time is a kinematic variable. Other quantities such as acceleration, velocity, and displacement are also associated with the motion of an object. For more details, you can refer to this resource.

End-Note:

Kinematic variables, including position, velocity, and acceleration, describe the state of rest or motion of a body. They are widely used in real-life applications such as mechanical engineering, biomechanics, and robotics to analyze the motion of engines, the human skeleton, or robots. To solve kinematics problems for any of these variables, you can use this online kinematics calculator, which helps perform accurate calculations for moving objects.

References:

From Wikipedia: General overview of Kinematics
From Khan Academy: Kinematic formulas & Equation of motion
From Physics Classroom: How to use kinematic equations