MEASUREMENT AND
DIMENSIONS
MOTION IN ONE-DIMENSION
MOTION IN ONE DIMENSION
Motion can be categorize into
three types:
Translational motion : A car
travelling on a highway is an
example of translational motion.
Rotational: The Earth’s spin on
its axis is an example of
rotational.
Vibrational Motion: the backand forth movement of a
pendulum is an example of
vibrational motion.
Position, Velocity and Speed
•The motion of a particle is
known, if the particle”s
position in space is known
at all times.
• A particle’s position is the
location of the particle with
respect to a chosen reference
point which is otherwise
considered the origin of a
coordinate system
• The displacement of a particle is
defined as its change in position in
some time interval
• As the particle moves from an
initial position xi to a final position
xf, its displacement is given by
x = xf - xi
• Distance –is the length of a path
followed by a particle
The Average Velocity (Vavg) of a particle
is defined as the particle’s displacement
divided by the time interval during
which that displacement occurs
where x indicates motion along the x-axis
• Average Speed Vavg of a particle is
defined as the total distance
travelled divided by the total time
interval required to travel that
distance:
• Thus, Average Velocity is the
displacement divided by the time
interval but average speed is the
distance divided by the time
interval.
Instantaneous Velocity &
Speed
• The Instantaneous Velocity
Vx equals the limiting value
of the ratio x/t as t
approaches zero.
• That is,
• The Instantaneous Speed of a
particle is defined as the
magnitude of its
instantaneous velocity
• A particle under constant
velocity moves with a
constant speed along a
straight line.
Acceleration
• When the velocity of a particle
changes with time, the particle is said
to be accelerating
• The average acceleration ax,avg of the
particle is defined as the change in
velocity Vx divided by the time
interval t during which that change
occurs:
Acceleration
• Dimension
• Instantaneous acceleration is
defined as limit of the average
acceleration as t approaches zero.
• That is the instantaneous
acceleration equals the
derivative of the velocity with
respect to time
Basic Terms in Translational Motion
A particle is a point-like
object that has mass but is of
infinitesimal size.
The displacement of a
particle is defined as its
change in position in some
interval of time.
Distance is the length of a path
followed by a particle.
The average velocity of a
particle is defined as the
particle’s displacement divided
by the time interval during
which that displacement occurs.
The average velocity of a
particle is defined as the
particle’s displacement
divided by the time interval
during which that
displacement occurs.
x
Vavg 
t
The average speed of a particle
is defined as the total distance
travelled divided by the total
time interval required to travel
that distance
POSITION AND DISPLACEMENT
• The location of a particle relative
to the origin of a coordinate
system is given by a position
vector r, which in unit notation is
Here
are the vector
components of position vector r, and x, y,
and z are its scalar components as well as
the coordinates of the particle. If a
particle moves so that its position vector
changes from
the particle
displacements
is given as
The displacement can also be written
as
If the position vector changes from r1 to
r2 then the particle’s displacement
during the time interval is
Using the unit vector notation, we can
rewrite this displacement as