One Dimensional Motion

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One Dimensional Motion

• Distance and Displacement
• Speed and Velocity
• Graphing Speed/Velocity
• Acceleration
• Free Fall

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Question of the Day

• Match each unit on the right with the type of
  measurement with which it would most likely be
  used.
• 1. Diameter of a Hydrogen atom a. Light-year
• 2. Distance from the Sun to Earth b. nanometer
• 3. Wavelength of a photon of visible light c.
  angstrom
• 4. Distance from our sun to the nearest star d.
  micron
• 5. Diameter of a red blood cell e.
  Astronomical unit

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The Answers..

• 1. C
• 2. E
• 3. B
• 4. A
• 5. D

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Choosing a Frame of Reference

• Before describing the motion of an object, you
  need to have a frame of reference.
• A frame of reference is a system of objects that
  are not moving relative (compared) to one
  another.
• The earth is a common frame of reference.

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Motion

• Motion is the change in the position of an
  object.
• When this change is compared to another object,
  it is called relative motion. The reference
  object can be either at rest or in motion.
• Linear motion is motion in a straight line.

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Measuring Distance

• Distance is the length of a path between two
  points.
• When an object moves in a straight line, the
  distance is the length of the line connecting the
  objects starting and ending points.
• Example Walk 5 meters, then walk 10 meters.

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Measuring Displacements

• Displacement is the direction from the starting
  point and the length of the straight line from
  the starting point to the ending point.
• Displacement is distance with a specific
  direction.
• Example Walk 5 miles north, then walk 10 miles
  southeast.
• See an example of distance vs. displacement

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Distance vs. Displacement
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Combining Displacements

• Displacements are added using vectors.
• A vector is a measurement that has a magnitude
  (number) and a direction.
• When two things occur in the same direction, the
  vectors add.
• When they act in opposite directions, they
  subtract.
• When added (or subtracted), the sum (or
  difference) is called the resultant vector.

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Combining Displacements
Start
5 m
10 m
7 m
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Question of the dayQuiz (10 pts)

• Please place all answers on a separate sheet of
  paper.
• 1. A student walks 3 blocks from his home to
  school, walks home for lunch, and then returns to
  school. What is (a) the total distance he
  walked, and (b) his overall displacement.
• 2. To get to a friends house, you make the
  following trip 5 blocks north, 7 blocks west,
  and 5 blocks south. (A) What distance did you
  travel? (B) how far away is your friends
  house?include distance AND direction!

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Speed

• Speed can be defined in a couple of ways
• How fast something is moving
• The distance covered in a certain amount of time
• The rate of change of the position of an object
• Units for speed are miles / hour (mi/hr)
• kilometers / hour (km/hr)
• feet / second (ft/s)
• This is the standard unit meters / second (m/s)

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Average and Instantaneous Speed

• Instantaneous Speed is the speed at any instant
  in time.

total distance covered time to travel that
distance
Average Speed
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During a typical trip to school, your car will
undergo a series of changes in its speed. If you
were to inspect the speedometer readings at
regular intervals, you would notice that it
changes often. The speedometer of a car reveals
information about the instantaneous speed of your
car that is, it shows your speed at a particular
instant in time.
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For each use of velocity described below,
identify whether it is instantaneous velocity or
average velocity.

• The speedometer on your car indicates you are
  going 65 mph
• A race-car driver was listed as driving 120 mph
  for the entire race.
• A freely falling object has a speed of 19.6 m/s
  after 2 seconds of fall in a vacuum.
• The speed limit sign says 45 mph.

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Calculating Speed
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d
t
V
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Example

• Sound travels at a speed of 330 m/s. If a
  firecracker explodes 3630 m away from you, how
  long does it take for the sound of the explosion
  to reach you?
• Speed, v 330 m/s distance, d 3630 m time, t
  ?
• So it takes 11 seconds for the sound of the
  explosion to reach you.

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Velocity

• Velocity is speed in a particular direction.
• 60 m/s north
• Constant Velocity does not change in speed or
  direction.
• Changing velocity can be a change in speed,
  direction, or both. Whenever there is a change
  in the velocity of an object, that object is said
  to be accelerating.

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Question of the DayVelocity Quiz

• If you are driving at 25 m/s and look out the
  window for 2.5 seconds, what distance have you
  traveled while looking out the window? (4 pts)
• To get from the gym to class, you walk a distance
  of 135 meters. If you walk at a speed of .65
  m/s, will you get to class in 4 minutes? (6 pts)

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Graphing Speed or Velocity

• When constructing a graph of speed or velocity,
  distance is plotted on the vertical, or y-axis,
  and time is plotted on the horizontal, or x-axis.
• The speed of an object can be found from the
  graph by calculating the slope of the line.

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Constant Speed Graph

• A distance-time graph for constant speed is a
  straight line.

How far did the person walk in 11 seconds? What
is her average speed? What is her instantaneous
speed at 8 seconds?
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Variable Speed Graph
How far did the person walk in 5 seconds? What is
her average speed? What is her instantaneous
speed at 5.5 seconds? At 7 seconds? When is she
walking faster - from 0-4 seconds or from 6-8
seconds?
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Question of the Day.Quiz (10 pts)

• A car travels 1200 m in 2 minutes. What is its
  average velocity in m/s? (3 pts)
• A sprinter runs 10 m in 30 seconds, then speeds
  up to 1 m/s for 1 minute.
• a) What is her average speed for the whole trip?
  (2 pts)
• b) What is her instantaneous speed at 45 sec? (2
  pts)
• c) Make a distance vs. time graph for this
  example (3 pts)

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Question of the DayAcceleration

• Write each of the following in your notebook.
  Circle each situation described below in which
  the object has an acceleration. For each one you
  circle, identify the direction in which the
  acceleration is acting.
• A car moves to the right while slowing down.
• A marble moves in a circular path inside a paper
  plate at a constant speed.
• The moon orbits the Earth.
• An air hockey puck moves smoothly across the air
  hockey table after being struck.
• A rocket is launched upward from the launch pad.

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Answers.

• yes, this is deceleration.
• Yes, this is centripetal acceleration
• Yes, also centripetal acceleration
• No, this is constant velocity
• Yes, this is acceleration

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Acceleration

• Acceleration is the rate at which velocity
  changes.
• Any time velocity changes, an object is
  undergoing an acceleration.
• A decrease in velocity is called deceleration.
• This change can be by speeding up, slowing down,
  or changing direction.

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Acceleration

• Units of acceleration are
• (miles / hour) / second mph/s
• (kilometers / hour) / second kmh/s
• (feet / second) / second ft/s2
• This is the standard unit (meters / second) /
  second m/s2
• Acceleration along the ground is horizontal
  acceleration.
• Vertical acceleration is called free fall.

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Calculating Acceleration

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Example

• A cars velocity at the top of a hill is 10 m/s.
  Two seconds later it reaches the bottom of the
  hill with a velocity of 26 m/s. What is the
  acceleration of the car?

The car is increasing its velocity by 8 m/s for
every second it is moving.
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Graphing Acceleration

• A velocity vs. time graph is used to find
  acceleration.

What is the final velocity of the car? What is
the instantaneous velocity of the car at 3
seconds? What is the acceleration of the car?
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Free Fall

• The acceleration of a falling object is due to
  the force of gravity between the object and the
  earth.
• Galileo showed that falling objects accelerate
  equally, neglecting air resistance.
• On the surface of the earth, in a vacuum, all
  objects accelerate towards the surface of the
  earth at 9.8 m/s2. This value is called g.

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Effect of Gravity on an Object
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Without Air resistance With Air resistance
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Gravity and an Accelerating Object

• Since the acceleration of gravity is 9.8 m/s2, an
  object increases (or decreases) its velocity by
  9.8 m/s each second.

What is the speed of the object after 3 seconds?
After 5 seconds? What is the acceleration of the
dropped object after 2 seconds? After 6
seconds? How would this graph change if the
object were thrown up into the air?
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Question of the DayQuiz (10 pts)
Complete the table below by drawing arrows to
indicate the directions of the objects velocity
and acceleration (remember its not always up and
down).