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Definition and Graphs of Motion, Vectors and Projectile Motion

Motion is defined as the act of changing location or position. Three types of motion exist: translational, oscillatory and rotational. Translational motions occur when a change in location takes place. Oscillatory motion is a motion that takes place without changing location. An example of such motion is the vibration Vibration A continuing periodic change in displacement with respect to a fixed reference. Neurological Examination of strings on a musical instrument. The rotational motion deals with the spinning of objects.

Last updated: Jul 28, 2022

Editorial responsibility: Stanley Oiseth, Lindsay Jones, Evelin Maza

Definition of Motion

Uniform linear motion

Uniform linear motion is a motion that occurs at a constant speed in one direction. It means that an object covers equal displacements in equal intervals of time. In this case, acceleration is 0. This type of motion can be described in the following terms:

$$v=\frac{s}{\Delta t}=const.$$

v ⇒ velocity (m/s)
s ⇒  displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms (m)
t ⇒ time (s)

Motion with uniform acceleration

This type of motion can be characterized by the changing velocity. The object is moving faster or slower, which means that acceleration does not equal 0 and remains constant. Motion with uniform acceleration can be described by 3 equations:

Displacement-time

$$s=0.5\times a\times t^{2}+ v_{0}\times t\times s_{0}$$

Velocity-time

$$s=a\times t\times v_{0}$$

s (or s0) ⇒ displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms (m)

a ⇒ acceleration (m/s2)

t ⇒ time (s)

v0 ⇒ velocity (m/s)

Free fall

Free fall is the motion of an object where the force of gravity is the only force acting upon it. The force of gravity is a constant parameter with an acceleration a = g = 9.81 m/s. Thus, free fall refers to motion with uniform acceleration. After neglecting air friction and lift, the following equations remain:

Free fall formula

g = 9.81 m/s

h ⇒ height

Uniform circular motion

In this type of motion, an object is moving along a circular path. Since the velocity is a vector, its constantly changing directions balance each other out. Thus, uniform circular motion is defined by the constant sum of velocity or to put it simply, if a car is driving in a circle with the speed of 50 km KM KM is the substrate concentration at which half-maximal velocity (½ Vmax) is reached (KM is measured on the x-axis while ½ Vmax is measured on the y-axis). Enzyme Kinetics/h, the acceleration is constant, yet the direction constantly changes.

Uniform circular motion formula
Gleichformige kreisbewegung1

Image by Lecturio.

ω ⇒ angular velocity (1/s)
α ⇒ angular acceleration (1/s2)
n ⇒ rotational speed (1/s)
r ⇒ radius Radius The outer shorter of the two bones of the forearm, lying parallel to the ulna and partially revolving around it. Forearm: Anatomy (m)
π ⇒ Pi (approx. 3.14)

Periodic motion

The periodic motion refers to changes in a system or a physical variable Variable Variables represent information about something that can change. The design of the measurement scales, or of the methods for obtaining information, will determine the data gathered and the characteristics of that data. As a result, a variable can be qualitative or quantitative, and may be further classified into subgroups. Types of Variables based on a fixed position that is repeated approx. or exactly in equal intervals of time. It can be described with the following variables:

$$T=\frac{1}{f}$$ $$ω=2\times\pi\times f$$

T ⇒ period, measured in seconds (s)
f ⇒ frequency, measured in hertz (Hz)
ω ⇒ angular velocity (1/s)

Graphs of Motion

The types of motion described above can be represented in the following graphs. Uniform linear motion is displayed in red, and motion with uniform acceleration is displayed in green.

Displacement-time graph

Displacement-time graph

Displacement-time graph

Image by Lecturio.

Velocity-time graph

Velocity-time graph

Velocity-time graph

Image by Lecturio.

Acceleration-time graph

Acceleration-time graph

Acceleration-time graph

Image by Lecturio.

Visualizing Kinematics

Definition

Kinematics is associated with the geometry of motion, and thus, it is a branch of mathematics. It begins with a description of the geometry of the system with the initial conditions of known values. These values depict the position, the velocity, and/or the acceleration of various points that are part of the system. Kinematics helps describe the motion of points, bodies, and groups of bodies without taking into account the masses of the objects or the forces that cause the motion.

Visualization aspect

Kinematics can be displayed using two-dimensional graphs. The plots would help understand the motion of the object with respect to time. Usually, 3 graphs are utilized: position graph, velocity graph, and acceleration graph.

The position graph displays the location of the object as time passes.
The velocity graph displays the speed of the object as time passes.
The acceleration graph displays how fast the object is moving as time passes.

The graph is two-dimensional, so it contains an x-axis and a y-axis. The x-axis represents time in seconds. The y-axis can represent any of the 3 items aboveposition (also called displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms), velocity, and acceleration.

Vectors

Definition

Vector is a quantity possessing both magnitude and direction. This quantity is different from a scalar quantity that has magnitude but no direction. For instance, if one checks the temperature, the result is a scalar quantity since temperature does not have direction. However, if one measures the wind, it is a vector quantity. The wind has both magnitude and direction since 30 mph from the west implies that the magnitude is 30 mph, and the direction is from the west.

Projectile Motion

Projectile motion is a form of motion in which an object (referred to as the projectile) is thrown near the earth’s surface moving along a curved path under the action of gravity only. In this case, air resistance Resistance Physiologically, the opposition to flow of air caused by the forces of friction. As a part of pulmonary function testing, it is the ratio of driving pressure to the rate of air flow. Ventilation: Mechanics of Breathing is treated as being negligible. The path the object takes is parabolic, with the only force acting on it being gravity (acceleration), which was stated before as equal to 9.8 m/sec2.

Components of projectile motion

The components in the x-axis and y-axis are calculated differently.

In the horizontal axis Axis The second cervical vertebra. Vertebral Column: Anatomy (x-axis), acceleration is 0 since neither wind nor air resistance Resistance Physiologically, the opposition to flow of air caused by the forces of friction. As a part of pulmonary function testing, it is the ratio of driving pressure to the rate of air flow. Ventilation: Mechanics of Breathing is present. The velocity in the horizontal axis Axis The second cervical vertebra. Vertebral Column: Anatomy will equal the initial velocity in the horizontal axis Axis The second cervical vertebra. Vertebral Column: Anatomy. The distance traveled in the horizontal axis Axis The second cervical vertebra. Vertebral Column: Anatomy ( displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms) can also be determined based on the time traveled. The following equations can be used:

ax = 0

(ax = acceleration in x-direction)

vx = v0x

(vx = velocity in x-direction, v0x = original velocity in x-direction)

x = x0 + v0x t

(x = displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms in x-direction, x= initial position, t = time)

In the vertical axis Axis The second cervical vertebra. Vertebral Column: Anatomy (y-axis), acceleration is equal to gravity. The velocity and displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms equations will be different since acceleration will affect Affect The feeling-tone accompaniment of an idea or mental representation. It is the most direct psychic derivative of instinct and the psychic representative of the various bodily changes by means of which instincts manifest themselves. Psychiatric Assessment the object in the vertical axis Axis The second cervical vertebra. Vertebral Column: Anatomy.

ay = -g

(ay = acceleration in y-direction, g = gravity)

vy = voy – g t

(vy = velocity in y-direction, voy = original velocity in y-direction, t = time)

y = yo + voy t – ½ g t2

(y = displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms in y-direction, y0 = initial position)

List of Parameters

t (or t0) Time (s)
v (or v0) Velocity (m/s)
s (or s0) Displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms (m)
a Acceleration (m/s2)
g = 9.81 m/s2 Acceleration of gravity (m/s2)
h Height (or falling height)
α Angular acceleration
s Arc length or displacement Displacement The process by which an emotional or behavioral response that is appropriate for one situation appears in another situation for which it is inappropriate. Defense Mechanisms (m)
r Radius Radius The outer shorter of the two bones of the forearm, lying parallel to the ulna and partially revolving around it. Forearm: Anatomy (m)
n Rotational speed (1/s)
v Velocity (m/s)
T Period, measured in seconds (s)
f Frequency, measured in hertz (Hz)
ω Angular velocity (the frequency of circular motion per second) (1/s)
Φ Exceeded angle
p Momentum (kg m/s or N s)
m Mass Mass Three-dimensional lesion that occupies a space within the breast Imaging of the Breast (kg)
F Force (N or kg m/s2)
I → Impulse (kg m/s)
Fav Average or net force (N or kg m/s2)
Ms Center of mass Mass Three-dimensional lesion that occupies a space within the breast Imaging of the Breast, no unit
M Torque (N m)
J Moment of inertia (kg m2)
r Axis Axis The second cervical vertebra. Vertebral Column: Anatomy of rotation Rotation Motion of an object in which either one or more points on a line are fixed. It is also the motion of a particle about a fixed point. X-rays
ρ Mass Mass Three-dimensional lesion that occupies a space within the breast Imaging of the Breast distribution
L Angular momentum [(kg m2)/s]
p Angular momentum of point-mass [(kg m)/s]
W Work (J or N m)
E Energy (J or N m)
P Power (W or J/s)
Δp Collision [(kg m)/s]
ρ Pressure (Pa or N/m2)
A Area of a surface (m2)
V Volume (mor L)

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