KINEMATICS: HISTORY, PRINCIPLES, FORMULAS, EXERCISES - PHYSICAL - 2025

The kinematics is (more specifically of classical mechanics) area of physics who cares to study the movement of bodies without taking into account the causes of it. It focuses on studying the trajectories of bodies over time through the use of magnitudes such as displacement, velocity, and acceleration.

Some of the issues covered by kinematics are the speed at which a train travels, the time it takes for a bus to reach its destination, the acceleration required by an airplane at the time of take-off to reach the necessary speed to take off, among other.

To do this, kinematics uses a coordinate system that allows the trajectories to be described. This spatial coordinate system is called the reference system. The branch of physics that deals with the study of movements taking into account their causes (forces), is dynamics.

History

Etymologically, the word kinematics has its origin from the Greek term κινηματικος (kynēmatikos), which means movement or displacement. Not surprisingly, the first record of studies on movement corresponds to the Greek philosophers and astronomers.

However, it was not until the fourteenth century when the first concepts on kinematics appeared, which are within the doctrine of the intensity of forms or theory of calculations (calculationes). These developments were made by scientists William Heytesbury, Richard Swineshead, and Nicolas Oresme.

Later, around the year 1604, Galileo Galilei carried out his studies on the movement in free fall of bodies, and of spheres on inclined planes.

Among other things, Galileo was interested in understanding how planets and cannon projectiles moved.

Contribution of Pierre Varignon

The beginning of modern kinematics is considered to have occurred with the presentation of Pierre Varignon in January 1700 at the Royal Academy of Sciences in Paris.

In this presentation he gave a definition of the concept of acceleration and showed how it can be deduced from the instantaneous velocity, using only differential calculus.

Specifically, the term kinematics was coined by André-Marie Ampère, who specified what the contents of kinematics were and placed it within the field of mechanics.

Finally, with the development by Albert Einstein of the Theory of Special Relativity, a new period began; This is what is known as relativistic kinematics, in which space and time no longer have an absolute character.

What do you study?

The kinematics focuses on the study of the movement of bodies without going into analyzing its causes. For this she uses the movement of a material point, as an ideal representation of the body in motion.

Beginning

The movement of bodies is studied from the point of view of an observer (internal or external) within the framework of a reference system. Thus, kinematics mathematically expresses how the body moves from the variation of the coordinates of the body's position with time.

In this way, the function that allows expressing the trajectory of the body not only depends on time, but also depends on speed and acceleration.

In classical mechanics space is considered as an absolute space. Therefore, it is a space independent of material bodies and their displacement. Likewise, it considers that all physical laws are fulfilled in any region of space.

In the same way, classical mechanics considers that time is an absolute time that passes in the same way in any region of space, regardless of the movement of bodies and any physical phenomenon that may occur.

Formulas and equations

Speed

Speed ​​is the magnitude that allows us to relate the space traveled and the time used to travel it. Velocity can be obtained by deriving position in relation to time.

v = ds / dt

In this formula s represents the position of the body, v is the velocity of the body and t is time.

Acceleration

Acceleration is the magnitude that makes it possible to relate the variation in speed with time. Acceleration can be obtained by deriving velocity with respect to time.

a = dv / dt

In this equation a represents the acceleration of the moving body.

Uniform line movement

As its name suggests, it is a movement in which the movement occurs in a straight line. Since it is uniform, it is a motion in which the velocity is constant and in which, therefore, the acceleration is zero. The equation of uniform rectilinear motion is:

s = s ₀ + v / t

In this formula s ₀ represents the initial position.

Uniformly accelerated rectilinear motion

Again, it is a movement in which the movement occurs in a straight line. Since it is uniformly accelerated, it is a movement in which the speed is not constant, since it varies as a consequence of acceleration. The equations of the uniformly accelerated rectilinear motion are as follows:

v = v ₀ + a ∙ t

s = s ₀ + v ₀ ∙ t + 0.5 ∙ at ²

In these v ₀ is the initial velocity and is the acceleration.

Exercise resolved

The equation of motion of a body is expressed by the following expression: s (t) = 10t + t ². Determine:

a) The type of movement.

It is a uniformly accelerated motion, since it has a constant acceleration of 2 m / s ².

v = ds / dt = 2t

a = dv / dt = 2 m / s ²

b) The position 5 seconds after starting the movement.

s (5) = 10 ∙ 5 + 5 ² = 75 m

c) The speed when 10 seconds have elapsed since the movement began.

v = ds / dt = 2t

v (10) = 20 m / s

d) The time it takes to reach a speed of 40 m / s.

v = 2t

40 = 2 t

t = 40/2 = 20 s

References

1. Resnik, Halliday & Krane (2002). Physics Volume 1. Cecsa.
2. Thomas Wallace Wright (1896). Elements of Mechanics Including Kinematics, Kinetics and Statics. E and FN Spon.
3. PP Teodorescu (2007). Kinematics. Mechanical Systems, Classical Models: Particle Mechanics. Springer.
4. Kinematics. (nd). In Wikipedia. Retrieved on April 28, 2018, from es.wikipedia.org.
5. Kinematics. (nd). In Wikipedia. Retrieved on April 28, 2018, from en.wikipedia.org.