Relative Motion
Motion in One Dimension
Motion in Two Dimension
Mechanics

the study of the motion of objects.
Kinematics

is the science of describing the motion of
objects using words, diagrams, numbers, graphs, and
equations.
Motion

is a change in
position
of an object with respect to
time and its
reference point
.
Relative Motion (Apparent motion)

The continuous
change of position of a body with respect to a second
body or to a reference point that is fixed.
All motion is relative to some frame of reference.
Whose moving?
Motion in
one dimension
, is motion in a
straight line or one direction.
x
0
x
Before describing motion, you must set up a
coordinate system
–
define an origin and a positive direction.
Describing Motion with Words
Scalars
are quantities that are described by a
magnitude
(or numerical value) alone.
Vectors
are quantities that are described by
both a magnitude and a direction.
Speed is a scalar quantity, but velocity and
acceleration are both vector quantities.
Practice
:
5 meters
5 meters north
20 degrees Celsius.
scalar
vector
scalar
Distance
is a
scalar quantity
that refers to
"how much ground an object has covered"
during its motion.
Displacement
is a
vector quantity
that refers
to "how far out of place an object is"; it is the
object's overall change in position.
Practice:
A person walks 5 m to the east and then
turns and walks 4 m to the west.
What is distance covered?
What is total displacement?
9 m
1 m
What is the distance and the displacement of
the race car drivers in the Indy 500?
Position = origin, start position.
Distance = 500 miles
Displacement = 0 miles
The location of an object in a frame of
reference is called
position (x)
. For straight
line motion, positions can be shown using a
number line.
The length traveled by an object moving in
any direction or even changing direction is
called
distance (d)
.
The separation between original and final
position is called
displacement (
Δ
x)
.
The motion of an object can be described by its
speed
,
velocity
, and
acceleration
.
The distance an object goes in a period of time
is its speed. ("how fast an object is moving.“)
If the speed of an object is
in a specific direction
,
it is called velocity. ("the rate at which an object
changes its position.“)
The change in velocity over a period of time is
the acceleration of the object. (“the rate at
which an object changes its velocity”)
Average Speed versus Instantaneous Speed
Instantaneous Speed

the speed at any given
instant in time.
Average Speed

the average of all
instantaneous speeds; found simply by a
distance/time ratio.
Practice
: Tom looks at his speedometer after
passing a speed limit sign.
At the end of his trip he calculates that he went
75 mi/hr the majority of the trip.
Calculating Average Speed and Velocity
Average Speed
–
Distance Traveled
v=d/t
Time of Travel
Average Velocity

Displacement
v=
Δ
x/t
Time
Remember to include direction when finding velocity
Practice
:
While on vacation in Arizona, Maria traveled a
total distance of 440 miles. Her trip took 8
hours.
What was her average speed? 55mi/hr
What was her average velocity?
55mi/hr West
Practice
:
A physics teacher walks 4 meters East, 2
meters South, 4 meters West, and finally 2
meters North. The entire motion lasted for 24
seconds.
Determine the average speed. 0.50 m/s
Determine the average velocity. 0 m/s
No displacement, No direction
Acceleration

is a vector quantity that is defined as the
rate at which an object changes its velocity.
speeding up
slowing down
changing direction
Example: Eric is running at a
constant velocity
of 2 m/s. Suddenly Joseph is on his heels and
Eric changes his velocity and begins running
at a velocity of 3 m/s and then 4 m/s. Now he
is well ahead of Joseph and keeps his pace at
4 m/s.
Eric had to accelerate to keep ahead of
Joseph, he had to
change his velocity
!
Constant Acceleration
–
A steady change in
velocity.
Example: Tina drops her bouncy ball from the
top of a tower.
Gravity
acts on her ball and
causes the ball to change its velocity every
second. The first second it accelerates to a
velocity of 10 m/s, then 20 m/s, 30 m/s, 40 m/s
until it hits the ground below. Her ball
accelerated at a constant acceleration of 10
m/s
2
.
Calculating the Average Acceleration
Acceleration values are expressed in units of
velocity/time. (Distance/time/time
or
d/t
2
)
Average Acceleration =
Change in Velocity
Time
a =
v
f
–
v
i
time
Objects in Free

Fall
A
free

falling
object is being acted upon only
by the
force
of gravity. There are two
characteristics that are true of free

falling
objects:
Free

falling objects do not encounter
air
resistance.
All free

falling objects (on Earth) accelerate
downwards at a rate of 9.8 m/s
2
or (10 m/s
2
).
•
The diagram at the right depicts
the acceleration of a free

falling
object.
•
The fact that the distance that
the object travels every interval of
time is increasing is a sure sign
that the ball is speeding up as it
falls downward.
Acceleration of Gravity (
g
)
Acceleration is the rate at
which an object changes its
velocity.
It is the ratio of velocity change
to time between any two points
in an object's path. To
accelerate at 9.8 m/s
2
means to
change the velocity by 9.8 m/s
each second.
A position versus time graph for a free

falling
object is shown below.
A velocity versus time graph for a free

falling
object is shown below.
Determining how fast an object has fallen
The formula for determining the
velocity
of a
falling object after a time of t seconds is:
v =
gt
Where g is the acceleration of gravity. The
value for g on Earth is 9.8 m/s
2
. The above
equation can be used to calculate the velocity
of the object after any given amount of time
when dropped from rest.
Determining how far and object has fallen
The
distance
that a free

falling object has
fallen from a position of rest is
also
dependent upon the time of fall.
Formula for finding distance fallen:
d = 1/2gt
2
Where g is the acceleration of gravity (9.8
m/s
2
on Earth).
Motion in
two dimensions
is motion in more
than one direction. Motion on the x and y
axes.
A
projectile
is any object that once projected
or dropped continues in motion by its own
inertia
and is influenced only by the
downward force of
gravity
.
Projectiles
move in two dimensions.
A
projectile
is any object that once projected or dropped
continues in motion by its own
inertia
and is influenced
only by the downward force of gravity.
There are the two components of the
projectile's motion

horizontal
and
vertical
motion.
Horizontally Launched Projectiles
Once launched, have no
horizontal
forces acting
on them.
Will maintain a constant
velocity. (neg. air resistance)
Will accelerate
vertically
due to gravity.
Solving Problems for horizontally launched
projectiles.
Equations:
▪
v=
gt
▪
d= 1/2 gt
2
▪
v= d/t
Non

Horizontally Launched Projectiles
Once launched, have no
horizontal forces acting
on them.
Will maintain a constant
velocity. (neg. air resistance)
Will accelerate vertically
due to gravity.
Solving Problems for Non

horizontally
launched projectiles.
Equations:
▪
v=
gt
▪
d= 1/2gt
2
▪
v= d/t
▪
d=
v
i
t
+ 1/2gt
2
▪
a
2
+ b
2
= c
2
▪
SOHCAHTOA
Practice:
Supposing a snowmobile is equipped with a flare launcher
that is capable of launching a sphere vertically (relative to
the snowmobile). If the snowmobile is in motion and
launches the flare and maintains a constant horizontal
velocity after the launch, then where will the flare land
(neglect air resistance)? In front, behind, or in the
snowmobile.
In the snowmobile.
Remember the flare
has the same velocity
as the snowmobile.
Practice:
Suppose a rescue airplane drops a relief package while it is
moving with a constant horizontal speed at an elevated
height. Assuming that air resistance is negligible, where will
the relief package land relative to the plane?
B.
Remember no forces
are acting in the horizontal
direction. The package
maintains the same velocity
as the plane.
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