Physics 1110: 1D Kinematics
Announcements:
•  CAPA homework due
tomorrow night!
•  Second CAPA Assignment
due Friday night.
•  This weeks tutorial (pages HW 3-6 ) is due at your
recitation at start of recitation.
Today we will finish chapter 2 of H+R
Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/
New Assignment Calendar on Webpage
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Clicker question 1
Set frequency to BA
Q. The graph show the positions position
train A
as a function of time for two trains
running on parallel tracks. Which
of the following statements is true?
train B
tC
time
A. Both trains speed up all the time.
B: At time tC, both trains have the same velocity.
C: Both trains have the same velocity at some time before tC.
D: At some time, both trains have the same acceleration.
E: 0 or 2 of the above statements are true.
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Clicker question 2
Set frequency to BA
Q. An object’s position vs time graph x
is shown. What best describes the
car’s velocity vs time?
v
v
A
B
t
v
t
v
C
t
t
D
E. None
of these
t
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Recap from Friday
Displacement is
Average velocity is
so
Instantaneous velocity is
Average acceleration is
Instantaneous acceleration is
for constant velocity
for constant acceleration
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Average velocity with constant acceleration
“Proof” that
when acceleration is constant
v(m/s)
In this example,
and
20
0
10 t(s)
Let us take an
average of equally
spaced points to
obtain the average
Avg for t=0,5,10:
Avg for t=0,2,4,6,8,10:
Can divide into smaller and smaller pieces until eventually
you have infinitesimal pieces to measure the average
Particle spends equal amounts of time below & above 10 m/s
Now do it more rigorously
Average velocity with constant acceleration
“Proof” that
when acceleration is constant,
v f = v 0 + at
or
at = v f − v 0
1 2
(v
t
+
at
)
0
vdt
(v
+
at)dt
∫
∫
0
0
0
2
v = t
=
=
t
t
∫€0 dt
t
t
1
v = v 0 + at = v 0 + (v f − v 0 ) /2
2
v0 + v f
v =
2
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Relation between velocity & acceleration
Examples of constant acceleration
v(m/s)
v(m/s)
v(m/s)
0
0
0
t(s)
Velocity starts at
0 and increases.
Acceleration > 0
t(s)
t(s)
Velocity starts at Velocity starts positive
0 and decreases. and decreases to 0
Acceleration < 0 and then decreases
more. Acceleration < 0
Acceleration is the change in velocity, not the velocity
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Clicker question 3
Set frequency to BA
A glider on a tilted air track is given a brief push uphill.
The glider coasts up to near the top end, stops, and then
slides back down. When the glider is at the highest point
of its path, its acceleration is..
A) straight down
C) upward along the track
acceleration is zero.
B) downward along the track
D) no direction, the
The direction of the acceleration vector is the direction of
the Δv vector
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Constant acceleration
For constant acceleration:
Setting t0 = 0 :
Remember:
For constant
acceleration:
(for constant acceleration only)
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Constant acceleration (continued)
Does
We know
We know
make sense?
which gives
which gives
For zero acceleration we get
which is
what we obtained for the constant velocity case
Seems to work!
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Another constant acceleration formula
(always true)
(constant acceleration)
Note that the acceleration
is absent from this equation
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Yet another constant acceleration formula
Solving
for
gives
Substitute into
to get
Subtract
and multiply by
to get
Rearrange terms to find
Note that the time is absent from this equation
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Gravity
The most obvious form of constant acceleration is from
the force of gravity. On the surface of the Earth gravity
causes a downward acceleration of magnitude 9.8 m/s2
which is labeled “g”:
Aristotle believed that heavier
objects fell faster than lighter objects
Galileo figured out that all objects
are subject to the same
acceleration, first by dropping balls
from the Tower of Pisa and later by
rolling balls down inclines
Gravity 0.5% higher at poles than equator and 0.2% 13
higher at Dead Sea (lowest) than Mt Everest (highest)
Clicker question 4
Set frequency to BA
Q. A ball is thrown straight up. At the top of its trajectory,
its acceleration is:
A.  zero
B.  straight up
C.  straight down
D.  depends on the ball mass
• At the top, the velocity is zero
• The acceleration due to gravity is
constant; it is always straight down
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Clicker question 5
Set frequency to BA
A rock is dropped from rest and falls a distance h (h > 0 ) to the
ground. Down is chosen as the positive direction and the origin
is placed at ground level.
What is y0 (the initial position) and
what is a (the acceleration)?
A) y0 = +h ,
B) y0 = –h ,
C) y0 = 0 ,
D) y0 = – h ,
E) y0 = 0 ,
a=–g
a=+g
a=+g
a=–g
a=–g
v0
=
0
h
0
+y
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Summary of constant acceleration equations
No displacement in this equation
No final velocity in this equation
No time in this equation
No acceleration in this equation
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Clicker question 6
Set frequency to BA
A rock is thrown downward with an initial speed |v0| from the edge
of a cliff. Assume no air resistance. It falls straight down and strikes
the ground after falling a distance h. A student is asked to compute
the final speed of the rock, just before it hits the ground. Which one
formula should she use?
A) v=v0 + a t
B) x=x0 + v0 t +(1/2) a t2
C) v2 = v02 + 2 a (x –x0)
D) None of these will work
E) More than one of these will work OK.
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Summary
•  Check the web site calendar.
•  Clickers counted today!
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