## The rectilinear movement

Movement is one of the physical phenomena that we most directly perceive, but the form of that movement depends on the place from which it is observed. It is the so-called “reference system (SR)”.

A reference system is a point and a system of axes, which we assume are fixed in the Universe, and which are taken to measure the distance where the object is located. While the path that describes an object which moves with respect to the reference system is the “path” that can be straight or curved.

The description of a movement requires knowing the place where it is (position) and the moment (instant). The instant is represented by the letter t, accompanied by some subscript if it is necessary, to indicate the place occupied by this data with respect to a set of measures. The fundamental unit in the International System is the second (s). The time elapsed between two instants is symbolized by the letters Δt, which is calculated: Bioprofe | The rectilinear movement | 01 The position has to report the situation of a mobile respect to an observer who is located in the Reference System (SR).

The displacement is the distance that exists between the final and initial position of a movement. It is always represented with a straight line and has a length that is determined by the difference between the final and initial positions of the selected time interval, which is known as the displacement module. In this way, the displacement is a vectorial magnitude, which means that it has an address, a direction and a module, which can be represented by an arrow and mathematically by a vector. Bioprofe | The rectilinear movement | 03

Path: Dashed line

Displacement: Continuous line.

The displacement between two instants t0 and t, corresponds to a vector that extends from the position in t0 to the position in t, it is symbolized by ∆x. Bioprofe | The rectilinear movement | 04

The velocity of an object is often confused with the speed. The velocity is physically a vector and it has a module (speed), a direction and a sense. The velocity with which a mobile is moving is the quotient between the space it travels and the time spent traveling it, being its fundamental unit in the International System the meter per second (m/s). Bioprofe | The rectilinear movement | 05

We can differentiate two types of speed:

• Average speed: It is the quotient between the displacement and the interval of time elapsed in performing that displacement.
• Instantaneuous speed: Speed that the body has at a specific time, at a certain point in its trajectory. It is obtained by making the limit of the average speed when the interval of the time considered tends to 0 or as the derivative of the vector of the position with respect to time.

Speed is the absolute value of velocista due to it can never be negative.

In a period of time Δt the mobile A has moved faster, and therefore with more speed, than the mobile B so it has traveled more space in the same period of time. Bioprofe | The rectilinear movement | 08

The value of the velocity of a mobile is modified by the action of acceleration, which depends on the interactions that other bodies exert on it. Its fundamental unit in the International System is the meter per second squared (m/s2). Bioprofe | The rectilinear movement | 09

Acceleration is also a vector and according to which aspect of the speed is modifies it receives a different name.

• Tangential acceleration: it modifies the speed of the movement.
• Normal acceleration: it modifies the direction of the movement.

There are two types of Rectilinear Movements:

• Uniform Rectilinear Movement, MRU.

If an object that is in motion has no acceleration, it describes a straight path (there is no normal acceleration that changes the direction of the velocitz) and the speed is constant (there is no tangential acceleration that modifies the velocity module), tenths its movement is uniform rectilinear. In this case the space traveled is equal to the displacement and its expression is: Bioprofe | The rectilinear movement | 10 Bioprofe | The rectilinear movement | 11

• Uniform Accelerated Rectilinear Movement, MRUA.

When a mobile describes a straight path but the speed is not constant, it is a rectilinear movement uniformly accelerated, due to the acceleration it has. Bioprofe | The rectilinear movement | 12

The obtained graphs for being able to differentiate both movements are:

Graphs Uniform Rectilinear Movement MRU Uniform Accelerated Rectilinear Movement MRUA
Position-instant Bioprofe | The rectilinear movement | 12 Bioprofe | The rectilinear movement | 13

Velocity-instant Bioprofe | The rectilinear movement | 14 Bioprofe | The rectilinear movement | 15

Acceleration-instant Bioprofe | The rectilinear movement | 16 Bioprofe | The rectilinear movement | 17

Freefall Movement.

It is the uniform accelerated rectilinear movement (MRUA) in which the acceleration coincides with the value of gravity. On the surface of the Earth, the acceleration of gravity can be considered constant, directed downwards, it is designated by the letter “g” and its value is 9,8m/s2  (sometimes it approaches to 10m/s2).

In this case the equations are:

To study Freefall movement we will normally use a reference system whose origin of coordinates is at the foot of the vertical of the point from which we release the body and we will consider the positive direction of the axis and pointing upwards.