Linear Motion

1
Linear Motion
2
Linear Motion

• All Motion is Relative
• This means when we describe motion we do it
  relative to something
• The Train is leaving the station or is the
  station leaving the train?

3
Linear Motion

• All Motion is Relative
• Even as we stand still
• Rotating (30o N) _at_ 1500 kilometers/h
• Revolving around sun _at_107,000 km/h
• Galaxy milling around _at_ 70,000 km/h
• Galaxy revolving _at_ 792,000 km/h
• Galaxy outward _at_ 2.1 million km/h

4
Linear Motion

• A car in the Indy 500 ends up at the same point.
• On the school bus traveling at 30mph you throw a
  ball to a classmate, how fast is the ball moving?
• We usually describe motion relative to the
  surface of the earth

5
Linear Speed

• Speed is a scalar quantity
• does not include direction.
• I am running at 10 mph, but I do not tell you
  where this is speed.
• Speed is my distance covered divided by the time
  it takes me

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Linear Speed

• mi/h (mph) Miles per hour
• km/h Kilometers per hour
• m/s Meters per second
• Light-years / century
• The symbol / is read as per

7

• Speed is a ____ quantity.
• A.) vector
• B.) scalar
• C.) additive
• D.) subtractive

8
A child walks 5.0 meters north, then 4.0 meters
east, and finally 2.0 meters south. What is the
magnitude of the resultant displacement of the
child after the entire walk? (A) 1.0 m (C) 3.0
m (B) 5.0 m (D) 11.0 m
9

• If I travel for 2 hours at 20 miles per hour the
  total distance covered is ?

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Linear Speed

• Speed
• Measure of how fast something moves
• Unit of distance divided by unit of time
• Two types of measurement
• Instantaneous speed
• Average Speed

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Linear Speed

• Instantaneous Speed
• You are in a car heading downtown, as you can see
  from the speedometer your speed is 40 mi/h.
• Downtown is 10 miles away at this speed, how long
  will it take you?
• IS THIS TRUE???

12
Linear Speed

• Average Speed
• It would take us a lot longer than 15 minutes to
  drive downtown because of the traffic where we
  have to slow, stop, start, accelerate, slow,
  stop, etc., etc,.

13
Linear Speed

• Average Speed
• Therefore in planning a trip we think about
  average speed
• Average Velocity
• Total distance (d) covered/ time (t)
• v d2 d1
• t

14

• If Downtown is 10 miles and
  it will take me 30 minutes when
  my average speed is 20 mi/h
• This is a lot different from an instantaneous
  speed of 40 mi/h.
• If we know our average speed and the time
  traveled we can arrange the formula to tell us
  our distance traveled.
• Total distance Avg speed x time
• d vt

15
Linear Velocity

• Velocity is a vector quantity
• this means is has Speed and Direction
• If a car travels at of 60 km/h we have defined
  its speed
• If we say it is traveling at 60km/h heading north
  we have defined its Velocity!

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• Going in a straight line at the same speed is
  called Constant Velocity.
• But if we change our speed (brake at a light) or
  our direction (turn a corner) then we have a
  Changing Velocity
• Changing our speed or direction is Acceleration

17

• Velocity has
• A) speed
• B) direction
• C) force
• D) A and B

18

• On a highway, a car is driven 80 kilometers
  during the first 1.00 hour of travel, 50
  kilometers during the next 0.50 hour, and 40
  kilometers in the final 0.50 hour. What is the
  cars average speed for the entire trip?
• (A) 45 km/h (C) 85 km/h
• (B) 60. km/h (D) 170 km/h

19
Linear Acceleration

• Acceleration is how quickly velocity changes
• a v2 v1
• t
• When we accelerate in a car from stop to 60km/h
  in 5 seconds.
• a (60 km/h 0 km/h)/5s
• 12 km/h/s

20
Linear Acceleration

• We have changed our speed and this is
  Acceleration.
• The same applies when we are in a car that slows
  this is called negative acceleration or
  Deceleration
• When we brake to a stop from 60km/h in 5 seconds.
• a (0 km/h 60 km/h)/5s
• 12 km/h/s

21

• Acceleration also applies to changes in
  direction.
• We feel the effects when in a car we are pushed
  to the side when we turn a sharp corner
• Acceleration is measured in km/hr/s, but usually
  m/s2 in Physics

22

• A skater increases her speed uniformly from 2.0
  m/s to 7.0 m/s in 12 seconds. What is her
  acceleration?
• For the next 20 seconds she continues at the same
  speed. What is her acceleration?
• She next applies her brakes and stops in 2
  seconds. What is her acceleration?

23

• A motocross rider accelerates from rest at 9
  m/s2 for 4.3 seconds. What is his final speed?
• As he approaches a curve he accelerates at -1.5
  m/s2 for 2.2 seconds. What is his new speed?

24
Free Fall How Fast

• If a rock is dropped off the side of
  a cliff we would expect it to
  fall and during the fall we would
  expect it to accelerate.
• If there was no air resistance its
  speed would increase by approximately 10m/s every
  second.

In m/s2, what would be its acceleration?
25
Free Fall How Fast

• After 5 seconds
• What would be its speed?
• v at
• v 10 m/s2 (5 s) 50 m/s
• Acceleration due to gravity is referred to as g
  and is accurately 9.8 m/s2

26
Time Velocity final vAvg y this second Total y
0 0 0 0 0





27
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5




28
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5
2 20 15 15 20



29
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5
2 20 15 15 20
3 30 25 25 45


30
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5
2 20 15 15 20
3 30 25 25 45
4 40 35 35 80

31
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5
2 20 15 15 20
3 30 25 25 45
4 40 35 35 80
5 50 45 45 125
32
Free Fall

• If the rock was thrown up into the air we would
  still see the rate of velocity change as -10m/s2.
• But for the first few seconds it would be
  decelerating, then stopped for a fraction of a
  second, before it started its acceleration toward
  the ground at 10m/s2.

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V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 30 0 0






34
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25





35
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40




36
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45



37
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45
4 -10 -5 -5 40


38
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45
4 -10 -5 -5 40
5 -20 -15 -15 25

39
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45
4 -10 -5 -5 40
5 -20 -15 -15 25
6 -30 -25 -25 0
40
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45
4 -10 -5 -5 40
5 -20 -15 -15 25
6 -30 -25 -25 0
7 -40 -35 -35 -35
41

• Acceleration due to gravity is approximately what
  value?
• A) 12 m/s2
• B) 9.8 m/s2
• C) 7 m/s2
• D) 0 m/s2

42

• A ball thrown vertically upward reaches a maximum
  height of 30 meters above the surface of Earth.
  At its maximum height, the acceleration of the
  ball is
• (A) 0.0 m/s2 (C) 9.8 m/s2
• (B) 3 m/s2 (D) 24 m/s2

43

• A ball thrown vertically upward reaches a maximum
  height of 30 meters above the surface of Earth.
  At its maximum height, the speed of the ball is
• (A) 0.0 m/s (C) 9.8 m/s
• (B) 3 m/s (D) 24 m/s

44

• A ball thrown vertically upward reaches a maximum
  height of 30 meters above the surface of Earth.
  The amount of time to teach its maximum height is
• (A) 0.0 s (C) 9.8 s
• (B) 3 s (D) 2.4 s

45

• Apollo 15 commander David R. Scott confirmed
  Galileo's hypothesis that in the absence of air
  resistance all objects fall with the same
  velocity.

46
Free Fall How Far?

• But there is air resistance on earth.
• So???
• Would you rather jump out of a plane with or
  without a parachute?
• Why?

47
Free Fall How Far?

• At the end of the first second of something
  falling is has a instantaneous speed of 10m/s.
• But this does not mean it has fallen 10m in the
  first second
• This is where the difference between average
  speed and instantaneous speed comes in
• It started at zero, so we know the average speed
  is somewhere between 0 and 10m/s

48
Free Fall How Far?

• The distance traveled by an object starting at
  rest and uniformly accelerating is
• d ½ gt2

49
Time Velocity final vAvg y this second Total y
0 0 0 0 0





50
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5




51
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5
2 20 15 15 20



52
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5
2 20 15 15 20
3 30 25 25 45


53
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5
2 20 15 15 20
3 30 25 25 45
4 40 35 35 80

54
Time Velocity final vAvg y this second Total y
0 0 0 0 0
1 10 5 5 5
2 20 15 15 20
3 30 25 25 45
4 40 35 35 80
5 50 45 45 125
55
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 30 0 0






56
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25





57
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40




58
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45



59
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45
4 -10 -5 -5 40


60
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45
4 -10 -5 -5 40
5 -20 -15 -15 25

61
V initial 30 m/s up
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45
4 -10 -5 -5 40
5 -20 -15 -15 25
6 -30 -25 -25 0
62
Time Velocity final VAvg Y this second Total Y
0 30 0 0
1 20 25 25 25
2 10 15 15 40
3 0 5 5 45
4 -10 -5 -5 40
5 -20 -15 -15 25
6 -30 -25 -25 0
7 -40 -35 -35 -35
63

• A sky diver free falls for twelve (12) seconds.
  What is her final velocity in m/s?
• Use g 10 m/s2
• Ignore air resistance

64

• A sky diver free falls for twelve (12) seconds.
  What is is the distance that she falls?
• Use g 10 m/s2
• Ignore air resistance

65

• Several years ago a car load of teenagers were
  coming down the Crest Highway too fast. They
  went off a cliff and fell 320-m (1050 feet). How
  long were they in the air before they crashed?
• Use g 10 m/s2
• Ignore air resistance

66
Air Resistance

• As we said before in a vacuum a stone and a
  feather will fall at the same rate.
• But we know here on Earth that does not happen
• If you were jumping out of a plane, what shape
  would you like your parachute to be?
• Why?