JUMP TO TOPIC
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