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Chapter 3
Linear Motion
1. MOTION IS RELATIVE
Everything moves, at least with
respect to some reference point.
To describe motion we shall talk about
Speed
Velocity
Acceleration
2. Speed
Instantaneous Speed
is the speed you would read
from a speedometer.
Average Speed = distance/time
Units - m/s, ft/s, etc.
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
miles
yet.driving
haven’t
been
for an hour yet?
3. Velocity




Average Velocity = Displacement/time
Units - m/s, ft/s, etc.
Instantaneous Velocity of an object
is its instantaneous speed plus the
direction it is traveling.
Velocity is a vector.
Displacement and Average Velocity
Distance traveled is the length of the path taken.
D  Displacement 
Average velocity =
 D
v
t

D
4. Acceleration
Acceleration = "change" in velocity/time
ft
m
Units –
s (m/s2), s (ft/s2), etc.
s
s
Acceleration is also a vector.
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 inclined planes to
study accelerations.
 He found constant accelerations
for inclines: the steeper the
incline, the greater the
acceleration. (It was too hard to
measure time for free-falls.)
 He also found that the size of
the objects didn't matter.
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.)
v0  0
2
a  3 ft/s
t  4s
v  at
v  3 ft /s ( 4 s )
2
v  12 ft / s
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
5. FREE FALL
Motion near the surface of the earth in
the absence of air resistance.
The acceleration of an object is
g = 32 ft/s2 = 9.8 m/s2.
How Fast
Velocity in gravitational field:
v = gt = 32t
How Far
d  vt
v
d t
2
gt
d t
(If initial velocity is zero)
2
d  gt  16t
1
2
2
2
BC and how deep is a well.
Michael Jordan – 3 s hang time??
Free Fall
Time of Fall
(s)
Velocity Acquired
(ft/s)
Distance Fallen
(ft)
1
32
16
2
64
64
3
96
144
4
128
256
5
160
400
Demonstrations


Demo - Coin and feather in vacuum
Film - Galileo's Experiment on the
Moon

Demo - Reaction timer

Demo - Paper and book drop
What is the acceleration of
an object at top of its
flight?
g, you should know this one.
Free Fall - How Quickly How
Fast Changes
Acceleration Is How Quickly How Fast
Changes.
 Acceleration is difficult to understand
because it is a rate of a rate.


What is a rate of a rate of a rate?
JERK
Chapter 3 Review Question
You throw a stone downward. It
leaves your hand with a speed of 10
ft/s. What is its speed two
seconds after leaving your hand?
(Neglect air resistance.)
(a) 10 ft/s
(b) 32 ft/s
(c) 42 ft/s
(d) 64 ft/s
(e) 74 ft/s
An object dropped from rest in
free fall will fall
feet in the
first second and
feet in
the second second.
(a) 16, 48
(b) 16, 32
(c) 32, 32
(d) 32, 64
(e) 32, 48