Phy 2053 Announcements
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Homework 0 (“intro to webassign”) due
tomorrow at 2am is practice and not for
credit. You can do it without having a
registration code (until Jan 18th).
Homework 1 due Jan 20 is posted in
webassign. It will count towards course grade.
SPS (past exams and solutions) will be
available at Target Copy for $20 probably by
next week
Clicker questions will count towards course
grade starting Jan .
Average vs. Instantaneous Velocity
Average velocity between
A and B

x

x

vaverage 
t
t
VAB = XAB/tAB = (Xf-Xi)/t = (54 m - 30 m)/10s = 2.2 ms-1
Instantaneous Velocity:
keep making t smaller:
x
t
The slope of the line tangent to the position-vs.time graph is defined to be the instantaneous
velocity at that time
Typical Homework Problem
2.19
Runner A is initially 4.0 mi west
of a flagpole and is running with a
constant velocity of 6.0 mi/h due east.
Runner B is initially 3.0 mi east
of the flagpole and is running with a
constant velocity of 5.0 mi/h due
west. How far are the runners from the
flagpole when they meet?
Let’s pick it apart
Acceleration
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Changing velocity means an
acceleration is present
Acceleration is the rate of change of the
velocity
v v f  v i
a

tf  ti
t
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Units are m/s² (SI), cm/s² (cgs), and
ft/s² (US Cust)
Vector quantity
Average Acceleration
Instantaneous acceleration
= slope of tangent of velocity-time graph
Position (m)
velocity (m/s)
acceleration (m/s2)
Acceleration
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a>0, v>0 or a<0,v<0 speed is increasing
v,a
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v,a
a>0,v<0, or a<0,v>0 the speed is decreasing
v
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a
a
v
A negative acceleration does not
necessarily mean the object is slowing
down
If the acceleration and velocity are both
negative, the object is speeding up
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Kinematic Equations
Used in situations with uniform
acceleration
v  v o  at
(1)
1 2
 x  v o t  at
2
(2)
2
(3)
2
o
v  v  2 a x
x  v average
 vo  vf
t
 2

t

Important: use the correct sign for x, v and a.
Some examples of Use
x  v average
Acceleration not in equation
 vo  vf
t
 2
Displacement not in equation:
v  vo  at
Final velocity not in equation :
1 2
x  v o t  at
2
Time not in equation :
v 2  vo2  2ax

t

Free Fall
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If only force on object moving near surface of
earth is gravity it is in free fall
Free fall is constant acceleration
The acceleration is called the acceleration due
to gravity, symbolized by g
g = 9.80 m/s²
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g is always directed downward
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When estimating, use g  10 m/s2
toward the center of the earth
Ignore air resistance and assume g doesn’t
vary with altitude over short vertical distances
Forces can apply to the object before or after the free fall
Free Fall options
• Initial velocity is zero
• Throw up -initial velocity
non-zero and positive—
instantaneous velocity at
maximum height = 0
• Throw down –initial
velocity is negative
• Starting and ending heights may
be equal – symmetric or
not equal-asymmetric - trajectory
v=0