# Kinematics: History, Principles, Formulas, Exercises

The **kinematics** is the physical area (specifically of classical mechanics) who cares to study the movement of bodies, regardless of the causes. It focuses on the study of the trajectories of bodies over time through the use of magnitudes such as displacement, velocity and acceleration.

Some of the issues addressed 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 a plane at takeoff to reach the speed needed to take off, among others.

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

__Story__

__Story__

Etymologically, the word kinematics originates from the Greek term *κινηματικος* ( *kynēmatikos* ), which means movement or displacement. It is not surprising that the first record of studies on motion corresponds to Greek philosophers and astronomers.

However, it was only in the 14th century that the first concepts on kinematics emerged, which are within the doctrine of the intensity of forms or the theory of calculations ( *calculations* ). These developments were made by scientists William Heytesbury, Richard Swineshead and Nicolás Oresme.

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

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

**Contributed by Pierre Varignon**

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

In this presentation, he defined the concept of acceleration and demonstrated how it can be deduced from instantaneous velocity using differential calculation alone.

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

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

**That studies?**

Kinematics focuses on the study of the movement of bodies without going in to analyze its causes. For this, it uses the movement of a material point, as an ideal representation of the moving body.

__Principles__

__Principles__

The movement of bodies is studied from the point of view of an observer (internal or external) within a frame of reference. Thus, kinematics mathematically expresses how the body moves by varying the coordinates of the body’s position over time.

Thus, the function that allows expressing the trajectory of the body depends not only on time, but also on velocity and acceleration.

In classical mechanics, space is considered to be an absolute space. Therefore, it is a space independent of material bodies and their displacements. It also assumes that all physical laws are enforced in any region of space.

Likewise, classical mechanics considers time to be 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__

__Formulas and Equations__

**Speed**

Speed is the magnitude that makes it possible to relate the space covered and the time needed to cover it. Velocity can be obtained by deriving position against time.

v = ds / dt

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

**Acceleration**

Acceleration is the magnitude that allows the velocity variation to be related to time. Acceleration can be obtained by deriving the velocity of time.

a = dv / dt

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

**Uniform rectilinear movement**

As the name implies, it is a movement in which the displacement takes place in a straight line. As it is uniform, it is a movement in which the velocity is constant and, consequently, the acceleration is zero. The equation of uniform rectilinear motion is:

y = y + v / t

In this formula, s represents the starting position.

**Uniformly accelerated rectilinear motion**

Again, it is a movement in which the displacement takes place in a straight line. Because it is uniformly accelerated, it is a movement in which the velocity is not constant, as it varies as a result of the acceleration. The equations of uniformly accelerated rectilinear motion are as follows:

v = v + a ∙ t

y = y + v + t + 0.5 ∙ in ^{2}

In these v is the initial velocity is already the acceleration.

__Exercise solved__

__Exercise solved__

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 as 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 after 10 seconds from the beginning of the movement.

v = ds / dt = 2t

v (10) = 20 m / s

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

v = 2t

40 = 2 t

t = 40/2 = 20 s