PHYS 1441 – Section 002
Lecture #5
Wednesday, Jan. 30, 2008
Dr. Jaehoon Yu
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Acceleration
Motion under constant acceleration
One-dimensional Kinematic Equation
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Motion under constant acceleration
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
1
Announcements
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• 3 point extra credit if done by midnight today, Wednesday, Jan. 30
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– http://www.uta.edu/physics/main/phys_news/colloquia/2008/Spring
2008.html
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Get your homework worked out but do not submit yet.
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If you see them again, do not submit answers but let me know of
the problem via e-mail
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
2
Special Problems for Extra Credit
• Derive the quadratic equation for yx2-zx+v=0
 5 points
• Derive the kinematic equation v  v0  2a  x  x0 
from first principles and the known kinematic
equations  10 points
• You must show your work in detail to obtain the full
credit
• Due next Wednesday, Feb. 6
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Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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3
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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Displacement, Velocity and Speed
Displacement
x  xf  xi
Average velocity
xf  xi x
vx 

tf  ti t
Average speed
Total Distance Traveled
v
Total Time Spent
Instantaneous velocity
vx  lim
Instantaneous speed
vx 
Wednesday, Jan. 30, 2008
Δt 0
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
x
t
lim
Δt 0
x
t
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Acceleration
Change of velocity in time (what kind of quantity is this?) Vector!!
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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Concept of Acceleration
The notion of acceleration emerges when a change in velocity
is combined with the time during which the change occurs.
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
8
Acceleration
Change of velocity in time (what kind of quantity is this?) Vector!!
•Average acceleration:
r
a
r
r
v f  vi
r
v

t
tf  ti
Wednesday, Jan. 30, 2008
analogous to
r
r r

x
x
f  xi
r
v  tf  ti  t
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
9
Definition of Average Acceleration
r
a
Wednesday, Jan. 30, 2008
r r
v v0
t  t0
r
v

t
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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Ex. 3: Acceleration and Increasing Velocity
Determine the average acceleration of the plane.
to  0 s
r
vo  0 m s
r
t  29 s v  260km h
r r
r
v  vo
260 km h  0 km h
km h
a
 9.0


29 s  0 s
s
t  to
9 1000m

 2.5 m s 2
3600 s  s
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
11
2.3 Acceleration
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
12
Ex.4 Acceleration and Decreasing Velocity
r
a
r r
v  vo

t  to
13m s  28 m s

12 s  9 s
5.0 m s
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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Deceleration is an Acceleration in the
opposite direction!!
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
14
Acceleration
Change of velocity in time (what kind of quantity is this?) Vector!!
•Average acceleration:
r
a
r
r
v f  vi
r
v

t
tf  ti
analogous to
r
r r

x
x
f  xi
r
v  tf  ti  t
•Instantaneous acceleration:
ax 
lim
Δt 0
vx
t
Wednesday, Jan. 30, 2008
analogous to
vx  lim
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
Δt 0
x
t
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Meanings of Acceleration
• When an object is moving at a constant velocity
(v=v0), there is no acceleration (a=0)
– Is there any net acceleration when an object is not
moving?
• When an object speeds up as time goes on,
(v=v(t) ), acceleration has the same sign as v.
• When an object slows down as time goes on,
(v=v(t) ), acceleration has the opposite sign as v.
• Is there acceleration if an object moves in a
constant speed but changes direction? YES!!
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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One Dimensional Motion
• Let’s start with the simplest case: the acceleration
is constant (a=a0)
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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Acceleration vs Time Plot
Constant acceleration!!
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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Equations of Kinematics
• Five kinematic variables
– displacement, x
– acceleration (constant), a
– final velocity (at time t), v
– initial velocity, vo
– elapsed time, t
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
19
One Dimensional Kinematic Equation
• Let’s start with the simplest case: the acceleration is constant (a=a0)
• Using definitions of average acceleration and velocity, we can derive
equation of motion (description of motion, position wrt time)
v  v0
a
a
t  t0
Solve for v
Wednesday, Jan. 30, 2008
Let t=t and
t0=0
v  v0
a
t
v  v0 at
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
20
One Dimensional Kinematic Equation
For constant acceleration,
simple numeric average
2v0  at
v  v0
1

 v 0  at
v
2
2
2
x  x0
v
t  t0
Let t=t and
t0=0
Solve for x
Resulting Equation of
Motion becomes
Wednesday, Jan. 30, 2008
x  x0
v
t
x  x0  vt
1 2
x  x0  vt  x 0  v 0t  at
2
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
21
Kinematic Equations of Motion on a
Straight Line Under Constant Acceleration
v  t   v0  at
Velocity as a function of time
1
1
x  x0  vt   v  v0  t
2
2
Displacement as a function
of velocities and time
Displacement as a function of
time, velocity, and acceleration
1 2
x  x0  v0t  at
2
v2  v02  2a  x  x0 
Velocity as a function of
Displacement and acceleration
You may use different forms of Kinematic equations, depending on
the information given to you in specific physical problems!!
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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How do we solve a problem using a kinematic
formula under constant acceleration?
• Identify what information is given in the problem.
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Initial and final velocity?
Acceleration?
Distance, initial position or final position?
Time?
• Convert the units of all quantities to SI units to be consistent.
• Identify what the problem wants
• Identify which kinematic formula is appropriate and easiest to
solve for what the problem wants.
– Frequently multiple formulae can give you the answer for the quantity you
are looking for.  Do not just use any formula but use the one that can
be easiest to solve.
• Solve the equations for the quantity or quantities wanted.
Wednesday, Jan. 30, 2008
PHYS 1441-002, Spring 2008
Dr. Jaehoon Yu
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