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Motion in One
Dimension
AKA… Linear Motion
One-Dimensional Motion
______________ motion takes place only in
one direction.
Example: The train can move either forward or
backward along the tracks. It cannot move left
or right.
In another words…
An object can move _______ or ________,
but not ____________ and _________ at
the same time.
Frame of Reference
______________ – a system for
specifying the precise location of
objects in space and time
“Another words, a reference point to
measure _________________.”
Example: ___________________
Distance
Is a _______ quantity
Has _________, but no _________
Measures the _______ between two
objects without indicating _______
from each other
Example: _____________________
Displacement
A _______ quantity
Has __________ and ___________
____________ – change in position of an object
Units: ___________
Displacement =
Example of Displacement
Displacement is _____ always equal to
the distance traveled.
Example if you walk three steps forward,
and three steps back… Your distance is
????
Your magnitude is _______!
Displacement Continued
Displacement can be ______ or ______
Unless otherwise stated,
Displacement to the right is ______
Displacement to the left is ______
Upward displacement is _______
Downward displacement is _______
Examples: _______________________
Can be Pos or Neg…
1. MOTION IS RELATIVE
Everything moves, at least with
respect to some reference point.
To describe motion we shall talk about
___________
___________
___________
2. Speed
___________ Speed
is the speed you would read
from a speedometer.
Average Speed = ___________
Units – _____________
Example of Average Speed
30 mph
A
2 miles
B
?
You take a trip from A to B and back
to A.
 You want to average 60 mph for the
round trip A to B to A.

From A to B you average 30 mph.
What is your average speed on the return trip from
B to A?
Example of Average Speed
30 mph
A
2 miles
?





60 mi/hr is 60 mi/(60 min) or 1 mi/min.
To average 1 mi/min for a 4 mi trip would require
4 min.
30 mi/hr is 30 mi/(60 min) or 1 mi/(2 min).
A 2 mi trip would take 4 min.
See a problem???
B
Speeding Little Old Lady
Sorry, Ma’am, but you
were doing 45 mph in a
30 mph zone.
Butokay,
I haven’t
Okay,
would
youdriven
believe45that I
milesbeen
yet. driving
haven’t
for an hour yet?
3. Velocity




Average Velocity =
______________
Units - _________________
Instantaneous Velocity of an object
is its _____________ plus the
__________ it is traveling.
Velocity is a _________.
Speed vs. Velocity
Velocity is NOT the same as speed.
Speed has ________ only (how fast)
Example: _______
Velocity has _______ and _______
Example: ____________
****
+/- can serve as a direction
Average Velocity
Units: meters per second, m/s
Average Velocity = change in position
change in time
Vavg = Δ x = xf − xi
Δt
t f − ti
Displacement and Average Velocity
Distance traveled is the length of the path taken.
D  Displacement 
Average velocity =
 D
v
t

D
Velocity can be interpreted
Graphically
When an object’s position is plotted
versus time, the _____ of a positiontime graph is the object’s velocity.
Instantaneous Velocity is
NOT Average Velocity
Instantaneous Velocity is the velocity
of an object at ________________
Example: When you glance down at
your speedometer while driving, the
speed indicated by the speedometer
is the magnitude of your
instantaneous velocity. (or how fast
you are going at that instant)
4. Acceleration
Acceleration = __________________
Units –
Acceleration is also a ________.
Has both magnitude and direction
Motion at constant velocity
Accelerated motion
Here
Here, too

Demo - Ball on incline and ball on table

We can sense acceleration by comparing
observations from a constant velocity frame of
reference to observations from an accelerating
frame of reference.

Interpretation - we can feel acceleration if
there is a “support” force or contact.
Acceleration on Galileo's
Inclined Planes
Velocity and Acceleration
 Galileo
used ____________ to
study accelerations.
 He found constant accelerations
for inclines: the _______ the
incline, the _______ the
acceleration. (It was too hard to
measure time for free-falls.)
 He also found that the size of
the objects ______ matter.
Average Acceleration
Average Acceleration =
aavg =
Units: ________
Determining Acceleration
Graphically
When a graph of an object’s velocity
over time is produced, the slope of
the _____________ graph is the
acceleration of the object.
When the velocity of an object is
constant, the acceleration is _____.
Velocity and Acceleration
An object with a + velocity and +
acceleration is __________
An object with a + velocity and acceleration is __________
An object with a - velocity and acceleration is __________
An object with a - velocity and +
acceleration is __________
Negative Values
A negative value for the acceleration
of an object does not always indicate
that the object is decelerating. If
the object is traveling in the negative
direction, a negative acceleration
would result in the object moving
________ in the _______ direction.
Relationships Between v
and a for Linear Motion.
v  v0
a
t
v  v0  at
v  v0  at
If initial velocity is zero, then
v  at
Example
A jogger starts at zero velocity with an
acceleration of 3 ft/s2. How fast is
she moving after 4 seconds? (Let’s
see if we can first do this without using
any equations.)
Chapter 3 Review
Questions
What is the average speed
of a horse that gallops a
round-trip distance of 15 km
in a time of 30 min?
(a) 0
(b) 0.5 km/h
(c) 30 km/h
(d) 500 m/s
(e) None of the above
What is the average velocity
for the round-trip of the
horse in the previous
question?
(a) 0
(b) 0.5 km/h
(c) 30 km/h
(d) 500 m/s
(e) None of the above
Some formulas relating to
displacement, velocity, and
acceleration:
Finding Displacement with Constant
Uniform Acceleration
∆x = ½ (Vi + Vf) ∆t
Finding Final Velocity with Constant
Uniform Acceleration
Vf = Vi + a∆t
Formulas Continued
Finding Displacement with Constant
Uniform Acceleration
∆x = vi∆t + ½ a (∆t)2
Finding Final Velocity after
Displacement
Vf2 = Vi2 + 2a∆x
5. FREE FALL
Motion near the surface of the earth in
the absence of air resistance, ______
___________________________.
The acceleration of an object is
g = __________ = _____________.
David Scott and the moon
David Scott demonstrated this on the
moon in 1971 when he dropped a
hammer and a feather at the same
time. Both the hammer and the
feather landed on the moon’s surface
at _____________ time.
A Ball thrown upward:
While its velocity is positive (up), the
acceleration on the ball is negative (down),
so the ball ____________ as it climbs.
At the top of the balls flight, its velocity is
reduced to zero, but its acceleration will
still be _________ (downward).
As the ball falls, its velocity is ______
(down) and its acceleration is ______
(down), so the ball ____________.