Describing Motion:

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Describing Motion Kinematics in One Dimension
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Sign Convention Direction
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Distance Displacement
Distance (x) equates
Displacement equates to
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Displacement
Displacement is written
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Example

• A person moves on the number line shown below.
  The person begins at B, walks to C, and then
  turns around and walks to A. For this entire
  range of motion DETERMINE
• the persons final position
• the displacement
• the distance.

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Speed Velocity
Speed How far
Velocity How
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Average Speed Velocity
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Example
A commuter drives 15.0km on the highway at a
speed of 25.0m/s, parks at work and walks 150m at
a speed of 1.50m/s from his car to his office.
(a) Determine the total time of the commute.
b) Determine the average speed of the entire
commute
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EXAMPLE
Usain Bolt holds the record for the 100m sprint
completing it in only 9.58s!
a) Determine his average speed in m/s. (1.6km
1mi)
Did he run faster than this at some point?
b) Mr Sample (I hold no record) ran the Philly
half-marathon (13.1mi) in 1hr55min36sec.
Determine my avg speed in mph.
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Example A woman starts at the entrance to a
mall and walks inside for 185m north for
10minutes. She then walks 59m south in 3minutes
to another store. She then leaves the store and
moves south 155m in 8minutes to reach her car
outside.
Determine her average velocity during the trip.
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Instantaneous Velocity
The instantaneous speed or velocity is how fast
an object is moving at a single point in time.
Does the gauge on your dashboard give you speed
or velocity?
Does this gauge give you an average or
instantaneous value?
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Acceleration
Acceleration is
Units?
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Constant Acceleration

• Constant acceleration implies what about
  velocity?
• Constant acceleration or deceleration implies
  what about distance?
• Acceleration of zero implies what about the
  velocity?

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Negative acceleration vs Positive acceleration
Both can equate to slowing down. When sign of
acceleration matches sign of velocity, object
speeds up in direction of that sign. When signs
oppose, object slows down in direction of v.
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Graphical Analysis of Motion
Position-time graph
Describes the position of object during a given
time period.
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Describe the position of the objects (A-D) over
time. Use origin in your statement.
x
A
E A S T
B
What does the intersection of A and B refer to?
0
t
WE S T
C
D
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Slope of x vs t graph
Recall that slope ?y / ?x
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Slope Interpretation
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Describe the velocity of the objects (A-D) over
time.
x
A
E A S T
B
0
t
WE S T
C
D
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What was the total distance traveled?
Example
What was the displacement for the entire trip?
What was the average speed for the first 6 sec?
What was the velocity of the object btw 2-4 sec?
What was the average velocity from B to E?
In which section(s) was there a constant
velocity?
In which section(s) was there a constant negative
velocity?
In which section had the maximum speed?
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Instantaneous velocity
Unlike vavg, instantaneous velocity occurs at a
single point. How would we find vinst at t
3.0s?
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At what time(s) does the cart have a zero
velocity?
Describe the velocity btw 0.0 - 0.80s?
Describe the velocity btw 2.6 - 3.2s?
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a) During what time periods, if any, is the
object's velocity constant?
b) At what time is its velocity the greatest?
c) At what time, if any, is the velocity zero?
d) Does the object run in one direction or in
both along its tunnel during the time shown?
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Graphical Analysis of Motion (2)
velocity-time graph
Describes the velocity of object during a given
time period.
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Describe the velocity of each object during its
motion, including initial velocity
V E L O C I T Y
A
B
time
C
D
Crossing t-axis ?
Intersection of lines on vt graph means ?
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Slope of v vs t graph
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Example
a) Determine the time(s) where object had -
acceleration
b) Determine the time(s) where object had
positive non-zero velocity
c) Determine the time(s) where object was at rest
d) Determine the time(s) where object had
constant velocity.
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Example
Determine acceleration of object between 4-9s
At what time(s) did object turn around?
During what time period(s) did object slow down?
When did object reach maximum speed?
When did object possess maximum acceleration?
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Instantaneous acceleration
Instantaneous acceleration occurs at a single
point. To find ainst at t 0.6s
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Constant Acceleration Eqns
We can write avg velocity 2 different ways
Combining the two eqns yields
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Constant / Uniform Acceleration Equations
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EXAMPLE
While driving along at 20m/s, you notice the
light up ahead turns red (110m away). Assuming
you have a reaction time of 0.5s,
a) How far from the light are you when you begin
to apply the brakes?
b) What constant acceleration will bring you to
rest at the light?
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EXAMPLE 2
A car starts from rest at a stop sign. It
accelerates uniformly at 4.0m/s2 for 6.0s, coasts
for 2.0s, and then slows down at 3.0m/s2 for the
next stop sign.
a) How far apart are the stop signs?
b) Determine the maximum velocity during the trip.
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v-t graphs part 2
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v-t graphs part 2
Determine the displacement of the object from
20s-38s.
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a vs t graph
a
0
t
We will only deal with constant accelerations.
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Reference Frames Relative Motion
Any measurement of position, distance, or speed
must be made
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In order to determine the speed of object moving
in a particular RF, we use subscripts
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VBG6m/s
VSG 20m/s
How fast is bike moving relative to bus?
VSG 20m/s
VCG -30m/s
How fast is bus moving relative to car?
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Falling Acceleration
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FREEFALL
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Anatomy of a upwardly thrown object
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EXAMPLE 1
A ball is thrown upward with an initial speed of
15.0m/s Assume negligible air resistance. 
a) Find the maximum height attained by the ball.
b) How much time does it take to reach the apex? 
c) Determine the velocity 2.2s into flight.
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EXAMPLE 2
As a part of a movie stunt a stunt man hangs from
the bottom of an elevator that is rising at a
steady rate of 1.10m/s.  The man lets go of the
elevator and freefalls for 1.50s before being
caught by the end of a rope that is attached to
the bottom of the elevator. 
(a) Calculate the velocity of the man at the
instant he is caught by the rope.  
(b) How long is the rope?
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EXAMPLE 3
An honors physics student stands at the edge of a
cliff that is 36m high. He throws a water
balloon straight up at 12.5m/s so that it just
misses the edge of the cliff on the way down.
Determine velocity of balloon as it strikes
ground below (many ways to solve)
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Collaborate with person next to you to answer
following questions
Three students are standing side-by-side next to
the railing on a fifth floor balcony.
Simultaneously, the three students release their
pennies.  One student drops a penny to the ground
below. The second student tosses penny straight
downwards at 15 m/s while third student tosses
penny straight upwards at 15 m/s. Assume
freefall.
a) Which penny or pennies strike(s) ground first?
b) Which penny or pennies strike(s) ground last?
c) Which penny or pennies strike(s) the ground
with the greatest final velocity?
d) Which penny or pennies strike(s) the ground
with the greatest acceleration?