Motion In One Dimension

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Motion In One Dimension
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One dimensional motion

• Motion in a straight line.
• No left or right motion
• Example
• Train traveling down straight track

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Frame of reference

• How fast is your desk moving?
• RELATIVE TO THE FLOOR AT REST
• RELATIVE TO THE SUN 30km/s
• Definition Coordinate system for specifying the
  precise location of objects in space.

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• Any frame of reference can be chosen, but must be
  consistent
• Some make explaining easier

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Displacement

• Change in position or ?x xf xi

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x xf xi
What is the geckos displacement?
Remember Delta represents change

• Displacement of Gecko
• ?x 85cm 22cm 63cm

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?y yf yi?y 60cm 30cm30cm upward
What is the geckos displacement if he climbed a
tree?
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Displacement is NOT always distance traveled

• What is the distance traveled by the gecko?

90cm
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BUT, displacement
y 60cm 30cm30cm up
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What would the geckos displacement have been if
he returned to the 20cm mark?

• Zero Displacement

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Displacement describes direction

• Positive right Negative left

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Distance and Displacement

• Distance is the length of the actual path taken
  by an object. Consider travel from point A to
  point B in diagram below

Distance d is a scalar quantity (no direction)
Contains magnitude only and consists of a number
and a unit.
(20 m, 40 mi/h, 10 gal)
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Distance and Displacement

• Displacement is the change in position.
• Must include magnitude and direction.

A vector quantity Contains magnitude AND
direction. (12 m, 300 8 km/h, N)
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Distance vs Displacement

• Draw the distance and displacement of a particle
  that moves from A to B around an oval track.

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Distance vs Displacement
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Speed

• How fast something is moving
• Rate at which distance is covered
• Distance covered per unit of time
• Ex km/s mi/h

Remember Rate is a clue that something is being
divided by time.
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Velocity
Speed in a given DIRECTION
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Average Velocity

• Positive or Negative
• Depends of sign of the displacement
• Time is always positive

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• Tile Board Time

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• Jessica drove 370km west (negative) on a straight
  highway to visit a friend. She left at 10a.m.
  and arrived at 3p.m. What is her average
  velocity?

Change in displacement ? -370km Change in time
????? 5.0h Average Velocity ? -74 km/h
Remember This is an average. Jessica didnt
travel exactly that speed the entire trip.
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During a race, Jason runs with an average
velocity of 6.02 m/s to the east. What
displacement does Jason cover in 137s?

• Ans 825m to the east

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If Matt rides south on his bicycle in a straight
line for 15 minutes with an average speed of 12.5
km/h, how far has he ridden?
Ans 3.1 km south
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A bus travels 280 km south along a straight path
with an average velocity of 88 km/h to the south.
The bus stops for 24 min, then it travels 210 km
south with an average velocity of 75 km/h to the
south.A. How long does the total trip
last?Ans A. 6.4 h
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A bus travels 280 km south along a straight path
with an average velocity of 88 km/h to the south.
The bus stops for 24 min, then it travels 210 km
south with an average velocity of 75 km/h to the
south.B. What is the avg. vel. for the total
trip? B. 77km/h south
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Graphically Interpreting Velocity
Remember the dropped ball experiment?
Why is this line curved?
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Graphically Interpreting Velocity
The amount of distance covered increases per unit
of time (second) as time goes along
15.33
6.47
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Slope Avg Vel
Must be a straight line
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Straight Line Graphs of 3 Different Objects
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Instantaneous may NOT be the same as average
velocity
Slope of tangent line Instantaneous velocity
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Tile Board Warm-UpDont write the question
Just show all your work

• A sprinter has been clocked at 9 s flat for
  the 100yd dash. (His coach has predicted an
  undefeated season.)
• A. How fast is he traveling in mi/h?
• B. Is this his final velocity?
• When do you think he would attain his greatest
  velocity?

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Givensx 100ydt 9 sec
11.11 yd 1 s
3600s 1h
3 ft 1yd
1 mi 5280ft
22.72 mi/h
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B. Is this his final velocity?C. When
do you think he would attain his greatest
velocity?

• B. NO, it is his average velocity.
• In theory, assuming all sprinters start from rest
  and continue to accelerate throughout the entire
  race, he should attain his greatest velocity as
  he crosses the finish line.

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Acceleration

• Who has the greater acceleration
• Logans Mousetrap Car doing 0 to 60mi/h in 3.9s
  (.00108 h)
• B. Micahs Mousetrap Car doing 0 to 60 mi/h in
  4.5s (.00125 h)
• SOLUTION
• Change in velocity is EQUAL 60 mi/h
• Time is DIFFERENT
• A. 60mi/h B. 60mi/h
• .00108h .00125h

Logans The WINNER
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Acceleration

• The RATE of change in velocity

Remember Rate is a clue that something is being
divided by time.
UNITS
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Best Accelerator of All Times
Quickest to change

• He could change
• directions on a dime
• speed quicker than anyone
• OSU 1988
• 2,628 rushing yds
• 39 touchdowns!!
• Super thighs Could squat 600 lbs!!!

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Tile Board Time
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Ans 2.2s
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ANS 2.0s
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With an average acceleration of -0.50 m/s2, how
long does it take a cyclist to bring a bicycle
with an initial speed of 13.5 m/s to a complete
stop?
ANS 27s
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• Suppose a treadmill has an avg accel.
• of 4.7 X 10-3 m/s2.
• How much does its speed change
• after 5.0 min?
• B.If the treadmills initial speed is
• 1.7 m/s, what will its final speed be?

A. 1.4m/s
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Suppose a treadmill has an avg accel. of 4.7 X
10-3 m/s2. B.If the treadmills initial speed is
1.7 m/s, what will its final speed be?
B. 3.1 m/s
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Acceleration has DIRECTION AND MAGNITUDE
A. Train takes off from station to the
east ?v ? accel
B. Train travels east at a constant
velocity ?v0 ? accel 0

• C. Train slows down
• as it nears a town
• ?v - ? accel -

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What if the train would have been moving to the
WEST

• v neg
• Acceleration neg

What if the graph continued and the velocity
became negative. What does this indicate about
the train?
Ans Slowed to 0 mi/h Started heading WEST
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Runaway Train

• If a passenger train is traveling on a straight
  track with a NEGATIVE velocity and a POSITIVE
  acceleration, is it speeding up or slowing down?

Time is increasing (positive) We arent going
back in time Hey, this isnt Back to the Future
Slowing Down
?v(-30mi/h)-(-50mi/h)
Must be a LARGER neg. So that ?v
Negative Velocity because its going to the WEST
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Test your Understanding
vi a Vf-Vi Motion
() () Speeding up
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vi a Vf-Vi Motion
- - (-) (-) Speeding up
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vi a Vf-Vi Motion
- () - () Slowing down
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vi a Vf-Vi Motion
- (-) (-) Slowing down
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vi a Vf-Vi Motion
-/ 0 SAME Constant velocity
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vi a Vf-Vi Motion
0 -/ (-/) 0 Speeding up from rest
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vi a Vf-Vi Motion
0 0 0 - 0 Remaining at rest
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Motion with Constant Acceleration
With Constant Acceleration vavg ?x vivf
?t 2
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Displacement with CONSTANT UNIFORM ACCELERATION

• vavg ?x vivf
• ?t 2
• ?x ½(vivf) ?t

?xdisplacement
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Givens ???
Now, solve it.
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Tile Board Time
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A car accelerates uniformly from rest to a speed
of 23.7 km/h in 6.5s. Find the distance the car
travels during the time.
Ans 21m
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A jet plane lands with a speed of 100 m/s and can
accelerate uniformly at a maximum rate of
-5.0m/s2 as it comes to rest. Can this plane
land at an airport where the runway is 0.80
km long?
Ans no, the plane needs 1 km
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Calculating Final Velocity
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Calculating Displacement with CONSTANT UNIFORM
ACCELERAION
vf
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Ans 36 km/h (9.9m/s) /-0.030km
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Ans -7.5 m/s 19m
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Calculating Final Velocity After Any
Displacement
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• ?t

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Tile Board Time
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Find the velocity after the stroller has traveled
6.32m.
Ans 2.51 m/s
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An aircraft has a liftoff speed of 120km/h. What
minimum uniform acceleration does this require if
the aircraft is to be airborne after a takeoff
run of 240m?
Ans 2.3 m/s2
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QUIZ TODAY
Do you know where theres 1. Constant
velocity? 2. Constant acceleration? 3. Zero
Velocity? 4. Negative velocity? 5. Negative
acceleration?
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SHOW ALL WORK

• Givens
• What are you solving for?
• Show numbers and UNITS plugged in
• Show entire answer and then
• Answer with correct SIG FIGS

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Falling Objects

• Free Fall Motion of an object falling with a
  constant acceleration (in a vacuum)
• g Symbol for free fall acceleration
• g 9.81 m/s2
• a -g -9.81 m/s2

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Free-Fall Speeds of Objects Dropped from Rest

• 0 seconds 0 m/s
• 1 second -10 m/s
• 2 second -20 m/s
• 3 second -30 m/s
• 4 second -40 m/s
• . .
• . .
• t -10t

Speed increases by -10 m/s each
second THEREFORE a -10 m/s/s Or a -9.81m/s2
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Instantaneous Speed for Falling Objects

• v a?t
• What would be the speedometer reading on a
  falling rock be 4.5s after it drops from rest?
  How about 8s after dropped? 100s?
• (use -10 m/s2 for convenience for this one)

Ans -45 m/s, -80 m/s, -1000m/s
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The rate at which speed changes is the
SAME whether the ball is going up or down.
ALWAYS -9.81 m/s2
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0 m/s -9.81 m/s2
0.69 m/s After 1s, velocity decreases 9.81 m/s
10.5 m/s -9.8 m/s2
-10.5 m/s -9.81 m/s2
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Moral of the StoryAcceleration Rate ALWAYS
EQUALS -9.81 m/s2 during free fall
Remember Straight line slope means constant
acceleration
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Jennifer hits a volleyball so that it moves with
an initial velocity of 6.0m/s straight upward.
If the volleyball starts from 2.0m above the
floor, how long will it be in the air before it
strikes the floor? Assume that Jennifer is the
last player to touch the ball before it hits the
floor.

• Givens
• vi 6.0m/s
• a-9.81 m/s2
• ?x -2.0 m

Pick Equation without TIME vf2vi2 2a?x
(6.0m/s)2 2(-9.81m/s2)(-2.0m) 75 m2/s2
vf -8.7 m/s vfvi a?t ?t (vf-vi)/a
(-8.7m/s 6.0 m/s)/- 9.81m/s2
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Can you catch the dollar bill?
It takes at least 1/7 of a second for the
necessary impulses to travel from the eye to the
brain to the fingersbut in only 1/8 s the dollar
bill has fallen 8cm, which is ½ the length of the
dollar bill.
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Test Your Reaction Time
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Homework Answersp. 65 1-5

• A. Decrease in positive direction ? zero ?
  Increase in negative direction
• B. Constant
• -11m
• -9.81 m/s2
• -9.81 m/s2
• Use vf2vi2 2a?x
• Since acceleration and displacement are the
  same, the vf is greater for the larger
• vi (4.0m/s) and her acceleration will be the
  same in each case.