This document provides an overview of key concepts related to motion, including definitions of terms like position, speed, velocity, acceleration, uniform motion, nonlinear motion, free fall, and circular motion. It explains that motion is always relative to a reference frame and discusses the differences between concepts like trajectory and displacement. Graphs and equations are presented for uniformly accelerated motion. The document aims to explain motion and related concepts at a foundational level.

1. MOTION
How do objects move and how do we explain it

2.  What is Motion?
 What is Motion and what is not?
 The Position Vector
 Trajectory versus Displacement
 What is Speed?
 What is Velocity?
 Linear Motion
 Nonlinear Motion
 Uniform Motion (UM)
A Guide to Motion

3.  Accelerated Motion
 What is Acceleration?
 Accelerated Motion Equations
 The UAM Graphs
 A Graphic Problem
 Free Falling Objects
 And now… one Question to Explain
 Circular Motion
 A Very Funny Motion
A Guide to Motion

4. What is Motion?
Are these aircrafts moving? How can we know it?

5. What is Motion?
Are these ships moving? How can we know it?

6.  Motion is change in an object’s position along time
 The idea needs a definition of position as the distance
to some reference frame (a point or axis)
 When position is fixed…
MOTION IS ALWAYS RELATIVE
 EVERY OBJECT MOVES REGARDING TO ANY POSSIBLE
REFERENCE FRAME
 Absolute motion or absolute rest make no sense at all,
THEY ARE IMPOSSIBLE
What is Motion and what is not?

7.  This is a 2D vector (a plane or flat vector)
 The vector goes from an origin position
(0,0) to the point expressed as (4,3)
 It means that the object placed at the
end of the vector (the arrow’s end) is 4
units away from axis OY and 3 units
away from axis OX
 We usually express a vector either with a
small or a capital letter (here “v”) with a
little arrow at the top
The Position Vector

8.  While trajectory is the path taken by a mobile along
time, displacement is the vector that expresses the
shortest distance between the origin and the end and
also the direction taken by the moving object
Trajectory versus Displacement

9.  Kinematic magnitude that measures which mobile is
faster, i.e., which mobile covers its path first or runs a
longer distance in the same time interval. It is a scalar
quantity defined as the distance covered divided by
the time interval. If we define it for a given interval,
then we find the average speed
 IS Unit : m/s (meters per second)
What is Speed?

10.  Kinematic magnitude defined with a vector that measures a
mobile’s speed taking into account not only its quantity but
also the direction in which the mobile runs. Velocity and
speed must not be confused, because speed is only the
velocity quantity without any direction. Velocity can also be
simply defined as the displacement (a vector quantity that
has a direction too) divided by the time interval.
IS Unit : m/s (meters per second) just like speed
What is Velocity?
!

11.  A mobile that holds a straight-line path
and follows no curves has a linear motion
Linear Motion

12.  A mobile that takes a curved path has a nonlinear
motion. According to the particular form of the curve,
it can be circular, parabolic, elliptical, etc.
Nonlinear Motion

13.  A mobile that runs at a constant speed, i.e., that covers equal
distances in equal time intervals has a uniform motion
 Equation to describe uniform motion in one dimension only:
x = x0 + v · (t – t0)
 It is a degree 1 equation, a linear equation when represented
on a graph (x versus t is a straight line)
 SLOPE or gradient is the vertical change divided by the
horizontal change for any part of the line (Here: Dx/Dt = v)
 A positive slope means that velocity is positive too, and a
negative slope means that velocity is negative
Uniform Motion (UM)

14.  A mobile with a non constant velocity, for it changes
in a time interval, has an accelerated motion
 Then we say the mobile has got an acceleration
 If it runs with a constant acceleration then we say
that it has a uniformly accelerated motion (UAM)
Accelerated Motion

15.  Kinematic magnitude defined as the rate at which the
velocity is changing, due to changes in speed and/or
direction. As a scalar quantity it can be defined by the
difference between final velocity and initial velocity,
divided by the time interval
IS Unit : m/s2 (meters per second each second)
What is Acceleration?

16.  Motion in one dimension has an equation to calculate velocity
(which is not constant) :
v = v0 + a · (t – t0)
 It is a degree 1 equation, a linear equation when represented on a
graph (v versus t is a straight line)
 A positive slope means that acceleration is positive too, and a
negative slope means that acceleration is negative
 There is another equation to calculate position:
x = x0 + v · (t – t0) + ½ a · (t – t0)2
 It is a degree 2 equation, a quadratic equation when represented
on a graph (x versus t is a curve called parabola)
Accelerated Motion Equations

17. The UAM Graphs

18. A Graphic Problem
What kind of motion has this mobile?

19.  When we drop an object and let it fall free it
holds an accelerated motion. In fact this
motion has a constant acceleration (UAM)
 Near to the Earth surface, falling acceleration
is constant and it is approximately 9.8 m/s2
 The value is known as GRAVITY
ACCELERATION and it depends on the mass
and size of our planet, that is why it has
different values for each planet
 For example, in the Moon objects fall with a
gravity acceleration of 1.6 m/s2
Free Falling Objects

20. And now…one Question to Explain

21.  A special curved path is a circumference. Its particular
feature is that IT HAS A CONSTANT RADIUS, so its
lengths equals: L = 2·p·r
 A special case of circular motion is UNIFORM CIRCULAR
MOTION (UCM)
 A mobile holds a UCM when it has a CONSTANT
ROTATIONAL SPEED (sometimes called ANGULAR SPEED
and symbolized as w)
 w is defined as: w = Dj/Dt and is measured in rad/s
 Relation between rotational (w) and linear or tangential
(v) speed: v = w·r
Circular Motion

22. A Very Funny Motion
where different passengers have a different speed... or not?
We usually describe this motion saying that THEY TURN AROUND and do
SOME REVOLUTIONS PER MINUTE (r.p.m.), where 1 rpm equals 2p/60 rad/s