Linear Motion

1
Chapter 2

• Linear Motion

2
Chapter 2

• Rate - any quantity divided by time
• -speed, velocity, acceleration
• Linear Motion - motion along a straight line path

3
Motion is Relative

• Everything that appears to be at rest is moving
  with respect to something else.
• A book sitting on the table is at rest relative
  to the table.
• A book sitting on the table is moving at 30km/s
  relative to the sun.
• All motion is relative to something else.
• A car travels 55mi/h relative to the road.
• A plane flies 200km/h relative to the earth.
• Assume, unless otherwise stated that speed is
  relative to the earth.

4
Speed

• Speed - the measure of how fast something is
  moving
• Speed distance/time rt d
• Units of speed- mi/h, km/h, m/s, knots
• Instantaneous speed - how fast something is
  moving at a given instant
• Think of driving down Henderson
• Your speed changes as you approach and leave stop
  lights and stop signs.
• Your speed at any instant is given to you as a
  reading on the speedometer.

5
Speed

• Suppose you are traveling constantly at 80km/h.
• How far do you travel in 1 hour?
• How far do you travel in 3 hours?
• How far do you travel in 1 minute?

6
Speed

• Average speed - the total distance covered per
  time interval
• Does not indicate variations in speed
• Average speed ?d/ ?t
• ? (delta) change in
• Average speed change in distance / change in
  time
• the slope of a position vs time graph
• http//www.physicsclassroom.com/mmedia/kinema/trip
  .gif

7
Speed

• You travel 800 km in 20 hours. What is your
  average speed?
• The odometer of a car reads 20.km at the
  beginning of a trip and 180km at the end of the
  trip. It took 2.0 hours and 30. minutes to make
  the entire trip. What was the average speed?
• Would it be possible to keep this average speed
  and not exceed 64km/h?

8
Velocity

• Velocity - speed in a given direction
• Must have two components
• Magnitude (speed)
• Direction
• Speed or Velocity?
• 4.5 miles per hour west
• 60 km/h
• 7.3 m/s northeast
• A car travels east at 55mi/h. Another car
  travels north at 55mi/h.
• Do the cars have the same speed?
• Do the cars have the same velocity?

9
Velocity

• Constant Velocity 2 requirements
• Constant Speed (no faster, no slower)
• Constant Direction (straight line path)
• Changing Velocity
• Either speed or direction or both are changing
• Constant speed along a curved path is changing
  velocity because the direction is changing at
  every instant
• In a car there are three controls that change the
  velocity
• Gas pedal
• Brake
• Steering wheel

10
Graphs of MotionUniform Velocity

• Describing motion using a position (distance) vs
  time graph
• Consider a car moving east with a velocity of
  10m/s
• The graph is linear because the velocity is
  constant
• The slope of a position vs time graph is the
  velocity.

11
Graphs of MotionUniform Velocity

• Describing motion with velocity vs time graphs
• Consider a car moving east with a positive
  constant velocity of 10m/s.
• The velocity is constanttherefore the graph is a
  horizontal line.
• The slope of a velocity vs time graph is
  acceleration. Velocity is constanttherefore the
  slope is 0 (there is no acceleration)

                                                
                                               
               
12
Graphs of Motion

• Velocity vs time graphs How can you tell if it
  is moving in a positive direction?
• The velocity is positive whenever the graph is in
  the positive region.
• The velocity is negative whenever the graph is in
  the negative region.

13
Distance or Displacement

• Distancehow far an object has traveled
• Indianapolis is about 45 miles away
• The distance to Indianapolis is 45 miles the
  distance back to Bloomington is 45 milesthe
  total distance traveled round trip is 90 miles
• Displacementhow far an object is from its
  original position (direction matters)
• The displacement to Indianapolis is 45 miles
  north the displacement back to Bloomington is 45
  miles souththe total displacement is 0 miles
• You can find displacement by
• Finding the area under a velocity time graph
• Using the equation d vavg t

14
Graphs of MotionSlope

• Looking at the slope of a position (distance) vs
  time graph...
• Slope Velocity
• As slope goes, so does velocity.
• If the velocity is constant, then the slope is
  constant (straight line).
• If the velocity is changing, then the slope is
  changing (curve).
• If the velocity is positive, then the slope is
  positive (moving upward, towards the right).
• If the velocity is negative, then the slope is
  negative (moving downward, towards the right).
• The steeper the line/curve, the faster the
  velocity.
• Looking at the slope of a velocity vs time graph
• Slope Acceleration
• If the graph is a horizontal line, there is no
  change in velocity, therefore there is no
  acceleration (the slope is 0).
• If the acceleration is positive, then the slope
  is positive (the line moves upward to the right).
• If the acceleration is negative, then the slope
  is negative (the line moves downward to the
  right).).

15
Graphs of MotionUniform Velocity

• The area under a velocity vs time graph is the
  displacement of the object.
• Find the distance traveled by each object.

16
Acceleration

• Acceleration the rate at which velocity is
  changing
• Acceleration ?v/ ?t
• Can increase or decrease (sometimes called
  deceleration)
• Think of traveling in a car, you can feel the
  acceleration
• 3 ways to accelerate in a car
• Brake pedalslowing down coming to a stop
  (changing speed)
• Steering wheelgoing around a corner or curve
  (changing direction)
• Gas pedalleaving from a stopped position
  (changing speed)

17
Acceleration

• Suppose you are traveling in a car and your speed
  goes from 10.km/h to 60.km/h in 2.0s. What is
  your acceleration?
• Suppose a car goes from 80.km/h to 15km/h in 5.0
  seconds. What is the acceleration?
• A car is coasting backwards down a hill at a
  speed of 3.0m/s when the driver gets the engine
  started. After 2.5s, the car is moving uphill at
  4.5m/s. Assuming that uphill is in the positive
  direction, what is the cars average
  acceleration?

18
Graphs of MotionUniform Acceleration

• Consider a car moving east with a changing
  velocitythe car is accelerating (speeding up).
• The velocity is changingtherefore the line has a
  slope (acceleration)

19
Graphs of MotionUniform Acceleration

• Now consider a car moving east that is
  accelerating. Notice the different graph.
• The car is acceleratingtherefore the velocity
  (slope) is not constant and the graph is a curve
  not a line

20
Graphs of Motion

• Velocity vs time graphs How can you tell if the
  object is accelerating or decelerating?
• Accelerating (speeding up) when the magnitude
  of the velocity is increasing
• Decelerating (slowing down) when the magnitude
  of the velocity is decreasing

21
Free FallA Case of Uniform Acceleration

• What makes an object fall?
• Gravitythe mass of the Earth is so great is has
  a strong gravitational pull that pulls objects to
  it
• Gravity also allows you to stand on the Earth
  without floating off into free space
• Gravity is the cause for satellite, moon and
  planet orbits
• Do heavier objects fall faster than lighter ones?
• Galileo found that, neglecting the effects of
  air, all freely falling objects had the same
  acceleration
• Masses do not matter
• Drop height does not matter
• The acceleration of a falling object is gravity
  (g) 9.80m/s2 (on Earth). We will use g 10
  m/s2 in most of our calculations (except for in
  labs or any other time when accuracy matters)
• Free Fall objects affected only by gravity

22
Free Fall

• An object in free fall accelerates at 10 m/s2
• The objects velocity increases by 10 m/s each
  second.
• Because the object is accelerating the distance
  it falls each second increases

23
Free Fall
How far?
How fast?
24
Free Fall

• A rock is dropped off a bridge and hits the water
  2.3 seconds later. The rock accelerates due to
  gravity at a rate of 10 m/s2.
• Using the water as the zero position and calling
  the upward direction positive, draw
  position-time, velocity-time and
  acceleration-time graphs for the rock.
• What is the rock's speed just before hitting the
  water?
• Determine the height of the bridge.
• King Kong carries Fay Wray up the 321 meter tall
  Empire State Building. At the top of the
  skyscraper, Fay Wrays shoe falls from her foot.
  How fast will the shoe be moving when it hits the
  ground?

25
Kinematics

• Kinematics is the science of describing the
  motion of objects using words, diagrams, numbers,
  graphs and equations.
• Equations
• vf vo at vf2 vo2 2a?d
• ?d vot ½ at2 ?d (vo vf)t/2
• Displacement how a far an object has moved from
  its original position (?d)
• Velocity the speed of an object in a given
  position (vf final velocity, vo initial
  velocity)
• Acceleration the rate at which an object
  changes velocity (a)
• Time (t)
• Solving Kinematics Problems
• Write down all the variables that are given to
  you what you need to solve for
• Compare these to the four kinematics equations to
  determine which equation should be used
• Be sure to use significant figures
• When computing (more than one operation) always
  round to one more sig fig than necessary until
  you achieve your final answer.

26
Linear Kinematics Problems

• Vivian is walking to the hairdressers at 1.3m/s
  when she glances at her watch and realizes that
  she is going to be late for her appointment.
  Vivian gradually quickens her pace at a rate of
  0.090m/s2. What is Vivians speed after 10.s?
• A race car traveling at 44m/s slows at a constant
  rate to a velocity of 22m/s over 11s. How far
  does it travel over this time?

27
Linear Kinematics Problems

• If a car accelerates from rest at a constant
  5.5m/s2, how long will it need to reach a
  velocity of 28m/s?
• A car accelerates at a constant rate from 15m/s
  to 25m/s while it travels 125m. How long does it
  take to achieve this speed?

28
Linear Kinematics Problems

• A driver of a car traveling at 15.0 m/s applied
  the brakes, causing a uniform acceleration of
  -2.0 m/s2.
• How long does it take the car to accelerate to a
  final speed of 10.0 m/s?
• How far has the car moved during the braking
  period?
• A boat accelerates uniformly from a velocity of
  6.5 m/s to the west to a velocity of 1.5 m/s to
  the west. If its acceleration was 2.7 m/s2 to
  the east, how far did it travel during the
  acceleration?

29
Kinematics Problems (Free Fall)

• The steamboat geyser at Yellowstone National
  Park, Wyoming is capable of shooting hot water up
  from the ground with a speed for 48.0m/s. How
  high can the geyser shoot?
• 2. A giraffe, which stands 6.00m tall, bites a
  branch off a tree to chew on the leaves, and he
  lets the branch fall to the ground. How long
  does it take the branch to hit the ground?

30
Kinematics ProblemsFree Fall

• 3. An object is thrown straight up with a
  velocity of 30.0m/s.
• As the object moves up, its acceleration is
  -10m/s2. For the velocity to be at zero, how
  long must the object be in the air?
• Is the acceleration 0 when the instantaneous
  velocity is 0?
• What is the acceleration of the object when it is
  on its way down?
• When are the instantaneous speeds the same?
• Are the velocities the same at this time?
• 4. A person throws a rock with an initial
  velocity of 14 m/s straight down off of a cliff.
  It takes 10.0 s for the rock to hit the ground.
• What is the rocks velocity as it hits the
  ground?
• How far does the rock travel?

31
Air Resistance and Falling Objects

• Feather vs Book
• Suppose you drop a feather and book from the top
  of the school at the same time
• Which will land first?
• Without air resistance they would both land at
  the same time.
• The effect of air resistance on the feather is so
  great, the book will land well before the
  feather.
• Which has the greatest air resistance?
• The book has a greater area and mass, therefore
  it displaces more air than the featherexperience
  greater air resistance.