1D motion: Kinematics

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Physics 2211 Lecture 4 Todays Agenda

• 1-D motion Kinematics
• Average Acceleration
• Instantaneous Acceleration
• Constant Acceleration
• Free fall

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• PRS Question 0
• What office hours are the best?
• (1) Mon, Thurs 400-530
• (2) Mon, Thurs 200-300
• Note I will be in tutorial lab (N-209) Wed 1-3
• and
• By appointment

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Average Acceleration

• Acceleration is the rate of change of
  velocity
• Average acceleration in the time

is
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Instantaneous Acceleration
Instantaneous acceleration a is defined as
For constant acceleration, there isnt any
difference between instantaneous acceleration a
and aavg since a aavg
constant
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THE BIG PICTUREs(t), v(t), a(t)
Position s, Velocity v and Acceleration a are all
functions of time.
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Special Case Constant Acceleration
Dt
Dv
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Velocity vs. Time
ax
(m/s2 )
Acceleration vs. Time
t
-5
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Relating Kinematic Equations to Graphs
a
a
v
v
v0

x
x0
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Relating Graphs
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Finding Velocity from Acceleration
(special caseconstant acceleration)
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Finding Position from Velocity
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Another Useful Equation
Solve for t and plug in
Simplify
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These formulae work for constant acceleration only
x
t
v
t
a
t
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Average Velocity
The displacement is the average velocity times
the time interval. (for constant acceleration
only)
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PRS Question 2
A ball thrown straight up reaches a highest
point and then falls straight down. At the
highest point,
y
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Solution
Going up the ball has positive velocity,
while coming down it has negative velocity. At
the top the velocity is momentarily
zero. Since the velocity is continually
changing there must be some acceleration. The
answer is (3) v 0, but a ? 0.
y
t
v
t
a
t
Note switch from x(t) to y(t)
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Free Fall
Constant acceleration due to gravity
y
t
v
t
y
a
t
a ? g
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ymax
A ball is projected directly upward with an
initial speed of 30 m/s. How high does it go and
how long does it take to get there?
v0
At apex v 0
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3 Ways to find ymax
(1)
(2)
(3)
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PRS Question 3

• The graph shows x(t) for two trains (A and B)
• running on parallel tracks. Which is true?

• Both trains have the same velocity at tt1
• Both trains speed up all the time.
• Both trains have the same velocity
• somewhere on the graph.
• 4. Both trains have the same acceleration
• somewhere on the graph.

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PRS Question 4

• The graph shows position vs. time for a particle
  moving along the x axis. At point B,

x
B
1. v gt 0 and a lt 0 2. v gt 0 and a gt 0 3. v lt
0 and a gt 0 4. v gt 0 and a 0 5. v lt 0 and a
lt 0
t
t1
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PRS Question 5

• The graph shows a(t) for 1D motion.
• If v(0) 5 m/s, when will the particle
• have a speed of 17 m/s?

• t 1 s (4) t 4 s
• t 2 s (5) t 5 s
• t 3 s (6) t 6 s

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PRS Question 6
x
The graph shows the motion of a particle moving
along the x- axis. At point P,
P
t
1. v gt 0 and a lt 0 2. v 0 and a gt 0 3. v lt 0
and a gt 0 4. v lt 0 and a 0 5. v gt 0 and a gt
0
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• The position of a particle is
• At what time(s) is the particles speed not
  changing?
• 1. t0 and t 22 s 2. t6 s
  5. t 11 s
• 3. t0 and t11 s 4. t0 s

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• Q An object moving along the x-axis has an
  acceleration
• for 0 lt t lt 10 s. At t0, the velocity is 40.0
  m/s and the position is 80.0 m. What is the
  objects position at t8 s?
• 1. 430 m 2. 360 m
• 3. 550 m 4. 490 m

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Recap

• Acceleration
• (Average, Instantaneous, Graphs)
  
• Constant Acceleration
• Free fall
• Constant Acceleration Problems
• Free Fall, Motion on Inclined Plane (Sections
  2.6-2.7)

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