Linear Motion

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Chapter 4 Linear Motion
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• You can describe the motion of an object by its
  position, speed, direction, and acceleration.

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I. Motion Is Relative (2.1) A. Everything moves.
Even things that appear to be at rest
move. 1. Motion is described by motion
relative to something else. a. Relative
to the sun, the center of the galaxy,
etc. b. We will discus motion (things in
our environment) relative to the surface of
the Earth.
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II. Speed (4.2) A. Speed is measure of how fast
something is moving (rate at which distance is
covered) 1. Rate term used to describe
something divided by time. 2. Speed Units
of distance / units of time (distance covered
per unit of time)
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3. Common Units a. miles/hour (mi/h) b.
kilometers/hour (km/h) c. meters/second (m/s)
Used in physics
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• Continental drift 2 mm/year (1mm one
  millimeter 10-3 meters)
• Walking speed 3 miles/hour 4.4 feet/second
  1.3 m/s (1m 1 meter, s seconds)
• Driving speed 60 miles/hr 100 km/hr 88 ft/s
  26 m/s
• Orbital speed (near Earth orbit) 8 km/s
  17,000 miles/hr
• Earth's speed around the sun 30 km/s
• Speed of light 300,000 km/s 186,000 miles/s.

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B. Instantaneous Speed the speed at any instant
(What you see on a cars speedometer)
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C. Average Speed total distance covered/time
interval   1. Does not indicate variations in
speed over time. 2. still describes rate at
which distance traveled
Total distance covered
Average speed
Time interval
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4.2 Speed

• think!
• If a cheetah can maintain a constant speed of 25
  m/s, it will cover 25 meters every second. At
  this rate, how far will it travel in 10 seconds?
  In 1 minute?

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4.2 Speed

• think!
• If a cheetah can maintain a constant speed of 25
  m/s, it will cover 25 meters every second. At
  this rate, how far will it travel in 10 seconds?
  In 1 minute?
• Answer In 10 s the cheetah will cover 250 m, and
  in 1 min (or 60 s) it will cover 1500 m.

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4.2 Speed

• think!
• The speedometer in every car also has an odometer
  that records the distance traveled. If the
  odometer reads zero at the beginning of a trip
  and 35 km a half hour later, what is the average
  speed?

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4.2 Speed

• think!
• The speedometer in every car also has an odometer
  that records the distance traveled. If the
  odometer reads zero at the beginning of a trip
  and 35 km a half hour later, what is the average
  speed?
• Answer

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D. Velocity (4.3) 1. Velocity and speed are
often used interchangeably, but in physics are
different. a. Velocity is speed in a given
direction.   b. Speed is how fast object moves
(direction does not matter)
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E. Constant Velocity must have constant speed
and direction 1. Object moves in straight
line 2. Objects path does not curve
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F. Changing Velocity 1. Velocity will change if
either speed or direction changes. 2. Constant
speed and constant velocity are not the same.
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4.3 Velocity

• think!
• The speedometer of a car moving northward reads
  60 km/h. It passes another car that travels
  southward at 60 km/h. Do both cars have the same
  speed? Do they have the same velocity?

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4.3 Velocity

• think!
• The speedometer of a car moving northward reads
  60 km/h. It passes another car that travels
  southward at 60 km/h. Do both cars have the same
  speed? Do they have the same velocity?
• Answer Both cars have the same speed, but they
  have opposite velocities because they are moving
  in opposite directions.

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III. Acceleration (4.4) A. acceleration is the
rate at which the velocity is changing 1.
applies to increases as well as decreases in
velocity. 2. decrease in velocity often
called deceleration or negative
acceleration
Change of velocity
Acceleration
Time interval
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B. Acceleration applies to changes in direction
as well as speed 1. When motion is in
straight line the term speed and velocity are
often used interchangeably.
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1. When motion is in straight line the term speed
and velocity are often used interchangeably.
Change of speed
Acceleration along a straight line
Time interval
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2. Units for acceleration a bit more complicated
Change of speed
Acceleration
Time interval
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4.4 Acceleration
Accelerate in the direction of velocityspeed up
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4.4 Acceleration
Accelerate in the direction of velocityspeed
up Accelerate against velocityslow down
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4.4 Acceleration
Accelerate in the direction of velocityspeed
up Accelerate against velocityslow
down Accelerate at an angle to velocitychange
direction
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4.4 Acceleration

• think!
• Suppose a car moving in a straight line steadily
  increases its speed each second, first from 35 to
  40 km/h, then from 40 to 45 km/h, then from 45 to
  50 km/h. What is its acceleration?

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4.4 Acceleration

• think!
• Suppose a car moving in a straight line steadily
  increases its speed each second, first from 35 to
  40 km/h, then from 40 to 45 km/h, then from 45 to
  50 km/h. What is its acceleration?
• Answer The speed increases by 5 km/h during each
  1-s interval in a straight line. The acceleration
  is therefore 5 km/hs during each interval.

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4.4 Acceleration

• think!
• In 5 seconds a car moving in a straight line
  increases its speed from 50 km/h to 65 km/h,
  while a truck goes from rest to 15 km/h in a
  straight line. Which undergoes greater
  acceleration? What is the acceleration of each
  vehicle?

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4.4 Acceleration

• think!
• In 5 seconds a car moving in a straight line
  increases its speed from 50 km/h to 65 km/h,
  while a truck goes from rest to 15 km/h in a
  straight line. Which undergoes greater
  acceleration? What is the acceleration of each
  vehicle?
• Answer The car and truck both increase their
  speed by 15 km/h during the same time interval,
  so their acceleration is the same.

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IV. Free Fall How Fast (4.5) A. The force of
Gravity causes object to accelerate
downward 1. If we disregard air resistance
(air friction) then free falling objects
only affected by gravity. Called free
fall 2. Use letter (g) to represent
gravity 3. gravity varies slightly around
the Earth. Average value is about 10
m/s2 4. More accurately, g is 9.8 m/s2
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B. The instantaneous speed of an object falling
from rest is equal to the acceleration multiplied
by the amount of time it falls. Instantan
eous speed acceleration x elapsed time  
(v symbolizes both speed and velocity)  
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1. speed decreases at the same rate with an
object moving upwards as it increases when moving
downward 2. An object thrown upward will reach a
velocity of zero when it gets to its highest
point    
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V. Free Fall How Far (4.6) A. Relationship
between distance traveled, acceleration, and
velocity       
Rearrange and solve for t
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4.5 Free Fall How Fast

• think!
• During the span of the second time interval in
  Table 4.2, the object begins at 10 m/s and ends
  at 20 m/s. What is the average speed of the
  object during this 1-second interval? What is its
  acceleration?

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4.5 Free Fall How Fast

• think!
• During the span of the second time interval in
  Table 4.2, the object begins at 10 m/s and ends
  at 20 m/s. What is the average speed of the
  object during this 1-second interval? What is its
  acceleration?
• Answer The average speed is 15 m/s. The
  acceleration is 10 m/s2.

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4.5 Free Fall How Fast

• think!
• What would the speedometer reading on the falling
  rock be 4.5 seconds after it drops from rest?
• How about 8 seconds after it is dropped?

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4.5 Free Fall How Fast

• think!
• What would the speedometer reading on the falling
  rock be 4.5 seconds after it drops from rest?
• How about 8 seconds after it is dropped?
• Answer The speedometer readings would be 45 m/s
  and 80 m/s, respectively.

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VI. Graphs of Motion A. Equations and tables not
the only way to describe relationships such as
velocity and acceleration. 1. Linear
relationship- e.g. speed and time a. Forms
straight line curve. b. Has constant slope
(direct proportion)       
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2. Parabolic relationship e.g. distance versus
time a. Not straight line. Curved
line b. Tangent at any point gives slope at that
point (slope of this curve is instantaneous
speed. Remember that slope is rise/run or
change in y over change in x. Distance/time
speed      
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VII. Air Resistance and Falling Objects
(4.8) A. Air resistance noticeably alters
the motion of things (like feathers, paper,
etc.) B. Less effect on more dense
(compact) objects C. Air resistance is
small enough to be neglected in most cases. 
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VIII. How Fast, How Far, How Quickly. How Fast
Changes (4.9) A. speed and velocity-used to
describe how fast something free falls from
rest. equation to use
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B. To specify how far the object has fallen we
are talking about distance.   equation to use
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What is this graph telling us?
Change in velocity over time acceleration
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C. Acceleration how quickly does speed or
velocity change 1. Very complex concept 2.
rate of a rate
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Constant Positive Velocity
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Constant Negative Velocity
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Positive Velocity and Positive Acceleration
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Positive Velocity and Negative Acceleration
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Motion Diagram




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Motion Diagram

Standing still

Moving constant speed

Speeding up

Slowing down
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• Particle Model
• Replace object with single point
• Simplified version of motion diagram

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Particle Model

Standing still


Moving constant speed


Speeding up


Slowing down

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Assessment Questions

• Jake walks east through a passenger car on a
  train that moves 10 m/s in the same direction.
  Jakes speed relative to the car is 2 m/s. Jakes
  speed relative to an observer at rest outside the
  train is
• 2 m/s.
• 5 m/s.
• 8 m/s.
• 12 m/s.

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Assessment Questions

• Jake walks east through a passenger car on a
  train that moves 10 m/s in the same direction.
  Jakes speed relative to the car is 2 m/s. Jakes
  speed relative to an observer at rest outside the
  train is
• 2 m/s.
• 5 m/s.
• 8 m/s.
• 12 m/s.
• Answer D

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Assessment Questions

• A gazelle travels 2 km in a half hour. The
  gazelles average speed is
• 1/2 km/h.
• 1 km/h.
• 2 km/h.
• 4 km/h.

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Assessment Questions

• A gazelle travels 2 km in a half hour. The
  gazelles average speed is
• 1/2 km/h.
• 1 km/h.
• 2 km/h.
• 4 km/h.
• Answer D

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Assessment Questions

• Constant speed in a constant direction is
• constant velocity.
• constant acceleration.
• instantaneous speed.
• average velocity.

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Assessment Questions

• Constant speed in a constant direction is
• constant velocity.
• constant acceleration.
• instantaneous speed.
• average velocity.
• Answer A

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Assessment Questions

• A vehicle undergoes acceleration when it
• gains speed.
• decreases speed.
• changes direction.
• all of the above

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Assessment Questions

• A vehicle undergoes acceleration when it
• gains speed.
• decreases speed.
• changes direction.
• all of the above
• Answer D

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Assessment Questions

• If a falling object gains 10 m/s each second it
  falls, its acceleration can be expressed as
• 10 m/s/s.
• 10 m/s2.
• v gt.
• both A and B.

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Assessment Questions

• If a falling object gains 10 m/s each second it
  falls, its acceleration can be expressed as
• 10 m/s/s.
• 10 m/s2.
• v gt.
• both A and B.
• Answer D

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Assessment Questions

• A rock falls 180 m from a cliff into the ocean.
  How long is it in free fall?
• 6 s
• 10 s
• 18 s
• 180 s

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Assessment Questions

• A rock falls 180 m from a cliff into the ocean.
  How long is it in free fall?
• 6 s
• 10 s
• 18 s
• 180 s
• Answer A

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Assessment Questions

• The slope of a speed-versus-time graph represents
• distance traveled.
• velocity.
• acceleration.
• air resistance.

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Assessment Questions

• The slope of a speed-versus-time graph represents
• distance traveled.
• velocity.
• acceleration.
• air resistance.
• Answer C

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Assessment Questions

• In a vacuum tube, a feather is seen to fall as
  fast as a coin. This is because
• gravity doesnt act in a vacuum.
• air resistance doesnt act in a vacuum.
• greater air resistance acts on the coin.
• gravity is greater in a vacuum.

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Assessment Questions

• In a vacuum tube, a feather is seen to fall as
  fast as a coin. This is because
• gravity doesnt act in a vacuum.
• air resistance doesnt act in a vacuum.
• greater air resistance acts on the coin.
• gravity is greater in a vacuum.
• Answer B

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Assessment Questions

• Speed and acceleration are actually
• one and the same concept, but expressed
  differently.
• rates of one another.
• entirely different concepts.
• expressions of distance traveled.

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Assessment Questions

• Speed and acceleration are actually
• one and the same concept, but expressed
  differently.
• rates of one another.
• entirely different concepts.
• expressions of distance traveled.
• Answer C