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Kinematics Equations

Last updated date: 28th Nov 2023
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Know More About Kinematics Equations

The goal of this first unit that is of the Physics classroom has been to investigate the variety which is of means by which the motion of objects can be described. The variety of representations that we have already learnt and investigated also includes verbal representations that are pictorial representations as well as the numerical representations and graphical representations that are the position-time graphs and velocity-time graphs.Define Kinematic Equations

The branch which is of physics that generally defines motion which is with respect to time and space that is ignoring the cause of that motion is known as kinematics. The equation which is the Kinematics is a set of equations that can derive an unknown aspect of motions of the body’s if the other aspects are provided.These equations link five kinematic variables:

The Displacement that is denoted by Δx.The initial velocity that is given as v0 which is said to be a Final velocity that is denoted by a v Time interval that is denoted by t Constant acceleration that is denoted by a.Essentially we can say that the kinematics equations which can derive one or more of these variables if the others are given. These equations which we have seen define motion at either constant velocity or at constant acceleration. Because we can say that the kinematics equations are only applicable at a constant acceleration or a speed which is constant we cannot use them if there is either of the two which is changing.

Kinematic Equation ParametersThe knowledge of each of the different quantities generally provides descriptive information about an object's motion.

For example, we can say that if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement that is of 264 meters. Then we can say that the motion of the car is fully described.If we take a second car then this is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, and the providing which is a final velocity of 24 m/s. The east and an eastward direction of displacement is 96 meters and then we can say that the motion of this car is fully described.These two statements which we have seen are to provide a complete description of the motion of an object. However, we can say that such completeness is not always known.It is often seen that only a few parameters of an object's motion are known while the rest are unknown. For example, we can say that as we approach the stoplight then we might know that the car has a velocity of 22 m/s, is moving in the east direction and is capable of a skidding acceleration of 8.0 m/s2 and to the direction which is west. However, we do not know the displacement that our car would experience if we were to slam on your brakes and skid to a stop. and then after that, we do not know the time required to skid to a stop. In such an instance like this, we can say that the unknown parameters that can be determined using physics principles and mathematical equations are the kinematic equations.What is Kinematics Equation?The equations that can be utilized for any motion that can be generally described as being either a constant motion which is of velocity motion that is an acceleration of 0 m/s/s or we can say a constant acceleration motion. They can be said to be never used over any time period during which the acceleration is changing. Each of the equations which are the kinematic equations includes four variables. If the values of three of the four variables are known to us then the value of the fourth varaiable can just be calculated.In this manner, we can say that the equation which is the kinematic equations provide a useful means of predicting information about an object's motion if other information is already known to us. For example, we can say that if the acceleration value and the initial and final which is of the velocity values of a skidding car is known then we can say that the displacement of the car and the time can be predicted using the kinematic equations. Here, we will focus upon the use of the kinematic equations that is to predict the numerical values of unknown quantities for objects in motion.

The four kinematic equations that describe an object's motion are given below:

d =\[ v_{i} \times t + \frac{1}{2} \times a \times t^{2}\] \[v^2_{f} = v^2_{i} +2\times  a \times d\]

\[v_{f} = v_{i} + a \times t\] d = \[\frac{v_{i} + v_{f}}{2} \times t\]

There are a variety of symbols that are used in the above equations that we have seen. Each symbol that we have seen has its own specific meaning. d stands for the displacement of the object, t stands for the time for which the object moved, a stands for the acceleration of the object, v stands for the velocity of the object, v, indicates that the velocity value is the initial while vf indicates that the value of the velocity that is final.Each of these four equations that we have seen appropriately describes the mathematical relationship which is between the parameters of an object's motion. As such we can say they can be used to predict unknown information which is about an object's motion that is if other information is known. In the next part we will investigate the process of doing this.

Kinematics- it's application

Kinematics is a  branch of physics that defines motion with respect to space and time, ignoring the cause of that motion. Kinematics equations are a set of equations that can derive an unknown aspect of a body’s motion if the other aspects are given

These kinematic equations are based on following factors:

  1. Displacement (denoted by Δx)

  2. Initial velocity 

  3. Final velocity 

  4. Time interval (denoted by t)

  5. Constant acceleration (denoted by a).

Kinematics aims to provide a description of the spatial position of bodies or systems of material particles, the rate at which the particles are moving (velocity), and the rate at which their velocity is changing (acceleration).

Kinematics is used in astrophysics to describe the motion of celestial bodies and systems; and in mechanical engineering, robotics and biomechanics to describe the motion of systems composed of joined parts (such as an engine, a robotic arm, or the skeleton of the human body).

The examples for kinematics are given below:

  1. Moving train and bus. 

  2. Motion of a mass on an inclined plane.

  3. Running water in the river. 

  4. Falling water from a mountain peak.

Kinematic gait analysis is the study of the motion of the body, limbs, and joints that occurs during movement. This method of analysis provides a non-invasive means of collecting objective information on joint and limb motion from patients.

The fundamental idea of kinematics is the discussion of the movement of objects, without actually taking into account what caused the movement to occur. By using simple calculus, we can find all of the equations for kinematics

For example, in machine components it is common to use kinematics analysis to determine the (unknown) speed of an object that is connected to another object moving at a known speed. For example, one may wish to determine the linear velocity of a piston connected to a flywheel that is turning at a known speed.

FAQs on Kinematics Equations

1.What are various variables in kinematics?

The various variables in kinematics depend on distance, displacement, speed, velocity, acceleration and jerk. Kinematics is not dependent upon the mass of an object, it only describes the motion of an object. It is totally descriptive and based on their observations, for example throwing off a ball, moving a train.

2.What are various laws of motion in kinematics?

There are usually various laws present in kinematics. The word line itself means motion. The various types of motion are:

  • Motion in One dimension

An example of motion in One dimension is linear or rectilinear motion.

  • Motion in two dimensions 

An example of two dimensions is the circulatory motion of projectile motion.

  • Motion  in three dimensions.

An example of three dimensions is gas molecules which move randomly in any direction.

3.From which standard onwards students learn about kinematics ?

Students learn about kinematics right from class seventh. Kinematics, which is also called motion, is related to physics. In 7th standard, students study about motion and various types of motion. At higher classes in 11th standard the students study kinematics in detail. In 11th standard they learn about kinematics, how kinetic and kinematics interrelated, what are various laws of motions, how is kinematics applicable in various other Sciences, How can kinematics be useful in robotics and space Technology.

4.What is motion studied in 7th standard and what are various types of motion?

Kinematics is nothing but about the study of motion. A body is known to be at rest if it does not change its position with time with respect to a reference point. For example a book lying on a table is at rest with respect to its surroundings. Hence the concept of motion and rest are interrelated. There are three main types of motion: rectilinear motion, circular motion and periodic motion.

5.State some interesting examples of kinematics which are applicable in real life?

Everything present in surroundings, moving right from running cars, trains or children playing in the ground, throwing a ball ,hitting a ball all these activities come under motion which is a part of kinematics .Kinematics are applicable in real life. They are not only applicable in physics but they are useful in mathematics for engineers for construction purposes. They are used by space research centers to analyze the movement of celestial objects. It is also useful for preparation of robots.

 some of the interesting examples of kinematics are :

  • moving train 

  • moving water in a river 

  • throwing a ball 

  • stone falling from a height

  •  rotating Blades of a fan

  •  kids sitting on merry go Round 

  • pendulum swings

  •  Even ball and socket joints present in the human body also work on the principle of kinematics.

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