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Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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PHYS 1441 – Section 002Lecture #5
Wednesday, Jan. 30, 2008Dr. Jaehoon Yu
• Acceleration• Motion under constant acceleration• One-dimensional Kinematic Equation• Motion under constant acceleration
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Announcements• E-mail distribution list: 32 of you subscribed to the list so far
• 3 point extra credit if done by midnight today, Wednesday, Jan. 30• I will send out a test message Thursday evening
– Need your confirmation reply Just to me not to all class please….
• Physics Department colloquium schedule at– http://www.uta.edu/physics/main/phys_news/colloquia/2008/Spring
2008.html• Phantom Submission problem started appearing on HW#2.
– Get your homework worked out but do not submit yet. – Let me delete and re-create the exact the same homework – I will do this for you to start submitting starting at 7pm tonight– If you see them again, do not submit answers but let me know of
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Special Problems for Extra Credit• Derive the quadratic equation for yx2-zx+v=0
5 points• Derive the kinematic equation
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
2 2
0 02v v a x x
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Displacement, Velocity and Speed
xx
vt
Δt 0lim
Displacement ixxx f
Average velocityt
x
tt
xxv
i
ix
f
f
Average speed Spent Time Total
Traveled Distance Totalv
Instantaneous velocity
Instantaneous speed xx
vt
Δt 0lim
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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AccelerationChange of velocity in time (what kind of quantity is this?) Vector!!
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs.
Concept of Acceleration
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Acceleration
a r
v ranalogous to
Change of velocity in time (what kind of quantity is this?)•Average acceleration:
f
f i
i
v v
t t
r rv
t
rf
f
i
i
x x
t t
r rx
t
r
Vector!!
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Definition of Average Acceleration
a r 0v v
r rv
t
r
0t t
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Determine the average acceleration of the plane.
0m so vr 260km hv
r0 sot 29 st
ar
Ex. 3: Acceleration and Increasing Velocity
o
ot t
v vr r
260km h 0km h
29 s 0 s
km h
9.0s
9 1000
3600
m
s s
22.5m s
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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2.3 Acceleration
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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ar
Ex.4 Acceleration and Decreasing Velocity
o
ot t
v vr r
13m s 28m s
12 s 9 s
25.0m s
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Deceleration is an Acceleration in the opposite direction!!
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Acceleration
xa xx
vt
Δt 0limanalogous to
Change of velocity in time (what kind of quantity is this?)
•Instantaneous acceleration:xv
t
Δt 0
lim
Vector!!
a r
v ranalogous to
•Average acceleration:
f
f i
i
v v
t t
r rv
t
rf
f
i
i
x x
t t
r rx
t
r
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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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 2008Dr. 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 2008Dr. Jaehoon Yu
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Acceleration vs Time Plot
Constant acceleration!!
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. 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 2008Dr. Jaehoon Yu
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• 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)
a
v
0
0
v v
t t
0v v
t
Let t=t and t0=0 a
Solve for v0v at
a
One Dimensional Kinematic Equation
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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One Dimensional Kinematic EquationFor constant acceleration, simple numeric average
v
x Resulting Equation of Motion becomes
v
x
0
2
v v 02
2
v at 0
1
2v at
0
0
x x
t t
0x x
t
Let t=t and t0=0 v
Solve for x
0x vt
0x vt 20 0
1
2x v t at
Wednesday, Jan. 30, 2008 PHYS 1441-002, Spring 2008Dr. Jaehoon Yu
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Kinematic Equations of Motion on a Straight Line Under Constant Acceleration
0v t v at
20 0
1
2x x v t at
0 0
1 1
2 2x x vt v v t
2 20 02v v a x x
Velocity as a function of time
Displacement as a function of velocities and time
Displacement as a function of time, velocity, and acceleration
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 2008Dr. 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.– 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.