8.1 The Language of Motion

1
8.1 The Language of Motion

• Many words are used when describing motion.
• Many of these words have specific meanings in
  science.
• Some common words used to describe motion
  include
• Distance
• Time
• Speed
• Position

• In short sentences, describe the motion of the
  soccer ball before and after it is kicked?
• What key words did you use when describing this
  situation?

See pages 8 - 9
2
Direction Makes a Difference

• Quantities that are measured or counted have a
  magnitude but may also contain a direction.
• Magnitude refers to the size of a measurement or
  the amount you are counting.
• Quantities that describe magnitude but do not
  include direction are called scalar quantities or
  just scalars.
• Example 25 seconds
• Quantities that describe magnitude and also
  include direction are called vector quantities or
  just vectors.
• Example 5 km North

Every time you use a map or give directions, you
are using vectors.
See page 10
3
Distance and Position

• Distance (d) is a scalar quantity that describes
  thelength of a path between two points or
  locations.
• Example A person ran a distance of 400 m.
• Position ( ) is a vector quantity that
  describes a specific point relative to a
  reference point.
• Example The school is 3.0 km East of my house.
• The SI unit for both distance and position is
  metres, m.

A car leaves home and drives 10 km to the store
and then returns home. The car has driven a total
distance of 20 km but its final displacement is 0
km.
See pages 10 - 11
4
Time Interval and Position

• Time (t) is a concept that describes when an
  event occurs.
• Initial time (ti) is when the event began.
• Final time (tf) is when the event finished.
• Time interval is the difference between the final
  and initial times.
• Time interval is calculated by

The time interval to move from the fire hydrant
to the sign is calculated by
The position of the sign is 7 m east of the tree.
See pages 11 - 12
5
Displacement and Distance

• Displacement describes the straight-line distance
  and direction from one point to another.
• Displacement describes how much an objects
  position has changed.
• Displacement is equal to the final position minus
  the initial position.
• The SI unit for displacement is metres, m.

Between 2 s and 5 s, the skateboarders displacem
ent is 5 m E. distance travelled is 5 m.
See page 12
6
Watch for Signs
When using vector quantities, opposite directions
are given opposite signs.
Between 0 s and 15 s the persons displacement is
Common sign conventions
10 m W 5 m E -10 m 5 m -15 m 15 m
W
What distance did the person walk in this same
time interval?
See page 13
7
Uniform Motion

• Objects in uniform motion travel equal
  displacements in equal time intervals.
• Objects in uniform motion do not speed up, slow
  down, or change direction.

The position of the ball in this photo is shown
at equal time intervals. How would you determine
if this motion is uniform motion?
See page 14
8
Graphing Uniform Motion

• Motion of an object can be analyzed by drawing a
  position-time graph.
• A position-time graph plots position data on the
  vertical axis (y axis) and time data on the
  horizontal axis (x axis).
• A best-fit line is a smooth curve or straight
  line that most closely fits the general shape
  outlined by the points.
• Uniform motion is represented by a straight line
  on a position-time graph.
• The straight line passes through all the plotted
  points.

A straight line passing through the plotted data
indicates uniform motion.
See pages 15 - 16
9
Slope

• The slope of a graph refers to whether a line is
  horizontal or goes up or down at an angle.
• Positive slope
• Slants up to the right.
• Indicates motion in the direction of the positive
  y axis.
• Zero slope
• Horizontal line.
• Indicates that the object is stationary.
• Negative slope
• Slants down to the right.
• Indicates motion in the direction of the negative
  y axis.

See pages 17 - 18
Take the Section 8.1 Quiz
10
8.2 Average Velocity

• Speed ( ) is the distance an object travels
  during a given time interval divided by the time
  interval.
• Speed is a scalar quantity.
• The SI unit for speed is metres per second
  (m/s).
• Velocity ( ) is the displacement of an object
  during a time interval divided by the time
  interval.
• Velocity describes how fast an objects position
  is changing.
• Velocity is a vector quantity therefore must
  include direction.
• The direction of the velocity is the same as the
  direction of the displacement.
• The SI unit for velocity is metres per second
  (m/s).

These two ski gondolas have the same speed but
have different velocities since they are
travelling in opposite directions.
See pages 26 - 27
11
Calculating the Slope of the Position-Time Graph

• The slope of a graph is represented by rise/run.
• This slope represents the change in the y-axis
  divided by the change in the x-axis.
• On a position-time graph the slope is the change
  in position ( ) divided by the change in time
  ( ).
• The steeper the slope the greater the change in
  displacement during the same time interval.

Which joggers motion has a greater slope? Which
jogger is moving faster?
See pages 28 - 29
12
Average Velocity

• The slope of a position-time graph is the
  objects average velocity.
• Average velocity is the rate of change in
  position for a time interval.
• The symbol of average velocity is
• On a position-time graph if forward is given a
  positive direction
• A positive slope means that the objects average
  velocity is forward.
• A negative slope means that the objects average
  velocity is backwards.
• Zero slope means the objects average velocity is
  zero.

See pages 28 - 29
13
Calculating Average Velocity

• The relationship between average velocity,
  displacement, and time is given by
• Use the above equation to answer the following
• What is the average velocity of a dog that takes
  4.0 s to run forward 14 m?
• A boat travels 280 m East in a time of 120 s.
  What is the boats average velocity?

See pages 31 - 32
Answers on the next slide.
14
Calculating Average Velocity

• The relationship between average velocity,
  displacement, and time is given by
• Use the above equation to answer the following
• What is the average velocity of a dog that takes
  4.0 s to run forward 14 m? (3.5 m/s forward)
• A boat travels 280 m East in a time of 120 s.
  What is the boats average velocity? (2.3 m/s
  East)

See pages 31 - 32
15
Calculating Displacement

• The relationship between displacement, average
  velocity, and time is given by
• Use the above equation to answer the following
• What is the displacement of a bicycle that
  travels 8.0 m/s N for 15 s?
• A person, originally at the starting line, runs
  west at 6.5 m/s. What is the runners
  displacement after 12 s?

See page 32
Answers on the next slide.
16
Calculating Displacement

• The relationship between displacement, average
  velocity, and time is given by
• Use the above equation to answer the following
• What is the displacement of a bicycle that
  travels 8.0 m/s N for 15 s? (120 m N)
• A person, originally at the starting line, runs
  west at 6.5 m/s. What is the runners
  displacement after 12 s? (78 m west)

See page 32
17
Calculating Time

• The relationship between time, average velocity,
  and displacement is given by
• Use the above equation to answer the following
• How long would it take a cat walking north at
  0.80 m/s to travel 12 m north?
• A car is driving forward at 15 m/s. How long
  would it take this car to pass through an
  intersection that is 11 m long?

See page 33
Answers on the next slide.
18
Calculating Time

• The relationship between time, average velocity,
  and displacement is given by
• Use the above equation to answer the following
• How long would it take a cat walking north at
  0.80 m/s to travel 12 m north? (15 s)
• A car is driving forward at 15 m/s. How long
  would it take this car to pass through an
  intersection that is 11 m long? (0.73 s)

See page 33
19
Converting between m/s and km/h

• To convert from km/h to m/s
• Change km to m 1 km 1000 m
• Change h to s 1 h 3600 s
• Therefore multiply by 1000 and divide by 3600
• or
• Divide the speed in km/h by 3.6 to obtain the
  speed in m/s.
• For example, convert 75 km/h to m/s.

Speed zone limits are stated in kilometres per
hour (km/h).
See page 33
20
Converting between m/s and km/h

• Try the following unit conversion problems
  yourself.
• Convert 95 km/h to m/s.
• A trucks displacement is 45 km north after
  driving for 1.3 hours. What was the trucks
  average velocity in km/h and m/s?
• What is the displacement of an airplane flying
  480 km/h E during a 5.0 min time interval?

See next slide for answers
See page 34
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Converting between m/s and km/h

• Try the following unit conversion problems
  yourself.
• 1. Convert 95 km/h to m/s. (26 m/s)
• 2. A trucks displacement is 45 km north after
  driving for 1.3 hours. What was the trucks
  average velocity in km/h and m/s?
• (35 km/h N, 9.6 m/s N)
• 3. What is the displacement of an airplane flying
  
• 480 km/h E during a 5.0 min time interval?
• (40 km E or 40, 000 m E)

See page 34
Take the Section 8.2 Quiz
22
9.1 Describing Acceleration

• We have already examined uniform motion.
• An object travelling with uniform motion has
  equal displacements in equal time intervals.
• Not all objects exhibit uniform motion.
• It is important to be able to analyze situations
  where the motion is not uniform.
• An object travelling with non-uniform motion
  will
• have different displacements during equal time
  intervals.
• take different amounts of time to travel equal
  displacements.
• have a continuously changing velocity.

As she slides, the velocity of the baseball
player is continually changing, therefore her
motion is non-uniform.
See pages 44 - 45
23
Positive and Negative Changes in Velocity

• A change in velocity ( ) occurs when the
  speed of an object changes, or its direction of
  motion changes, or both.
• A change in velocity can be calculated by
• If the change in velocity is the same sign (, -)
  as the initial velocity, the speed of the object
  is increasing.
• If the change in velocity is the opposite sign
  (, -) of the initial velocity, the speed of the
  object is decreasing.
• If the change in velocity is zero, the object is
  travelling with uniform motion.

If forward is designated positive, this
dragsters change in velocity is positive.
If forward is designated positive, this landing
shuttle has a negative change in velocity.
See page 46
24
Acceleration

• Acceleration is the rate of change in velocity.
• This change in velocity can be due to a change in
  speed, a change in direction, or both.
• Two objects with the same change in velocity can
  have different accelerations.
• This is because acceleration describes the rate
  at which the change in velocity occurs.

Suppose both of these vehicles, starting from
rest, speed up to 60 km/h. They will have the
same change in velocity but since the dragster
can get to 60 km/h faster than the old car, the
dragster will have a greater acceleration.
See pages 47 - 48
25
Positive and Negative Acceleration

• The direction of the acceleration is the same as
  the direction of the change in velocity.
• Acceleration that is opposite the direction of
  motion is sometimes called deceleration.
• Examples of accelerations
• 1. A car speeding up in the forward direction.
• If we designate the forward direction as positive
  () then the change in velocity is positive (),
  therefore the acceleration is positive ().

See pages 49 - 50
26
Positive and Negative Acceleration

• Examples of accelerations
• 2. A car slowing down in the forward direction.
• If we designate the forward direction as positive
  () then the change in velocity is negative (-),
  therefore the acceleration is negative (-).

See pages 49 - 50
27
Positive and Negative Acceleration

• Examples of accelerations
• 3. A car speeding up in the backward direction.
• If we designate the backward direction as
  negative (-) then the change in velocity is
  negative (-).
• This means that the acceleration is negative (-)
  even though the car is increasing its speed.
  Remember positive () and negative (-) refer to
  directions.

See pages 49 - 50
28
Positive and Negative Acceleration

• Examples of accelerations
• 4. A car slowing down in the backward direction.
• If we designate the backward direction as
  negative (-) then the change in velocity is
  positive ().
• This means that the acceleration is positive ()
  even though the car is decreasing its speed.
  Remember positive () and negative (-) refer to
  directions.

See pages 49 - 50
Take the Section 9.1 Quiz
29
9.2 Calculating Acceleration

• The acceleration of an object is dependent upon
  the change in velocity and the time required to
  change the velocity.
• When stopping a moving object, the relationship
  between time and acceleration is
• Increasing the stopping time decreases the
  acceleration
• Decreasing the stopping time increases the
  acceleration

Airbags cause the person to slow down in a longer
period of time compared to hitting a solid
object, such as the dashboard. This increased
time results in a smaller deceleration.
See page 56
30
Velocity-Time Graphs

• The motion of an object with uniform motion is
  best represented by a position-time graph.
• The motion of an object with a changing velocity
  is best represented by a velocity-time graph.
• The slope of a velocity-time graph is average
  acceleration.
• Acceleration is measured in m/s2.

The slope of a velocity-time graph is the average
acceleration of the object.
See pages 57 - 58
31
Determining Motion from a Velocity-Time Graph

• A velocity-time graph can be analyzed to describe
  the motion of an object.
• Positive slope (positive acceleration) objects
  velocity is increasing in the positive direction.
• Zero slope (zero acceleration) objects
  velocity is constant.
• Negative slope (negative acceleration) objects
  velocity is decreasing in the positive direction
  or the objects velocity is increasing in the
  negative direction.

• During which time interval was
• The acceleration zero?
• The acceleration negative?
• The acceleration positive?
• The object increasing its velocity north?
• The object decreasing its velocity north?
• The object moving at a constant velocity north?

Answers on next slide
See pages 58 - 59
32
Determining Motion from a Velocity-Time Graph

• During which time interval was
• The acceleration zero? (t1 to t2)
• The acceleration negative? (t2 to t3)
• The acceleration positive? (0 to t1)
• The object increasing its velocity north? (0 to
  t1)
• The object decreasing its velocity north? (t2 to
  t3)
• The object moving at a constant velocity north?
  (t1 to t2)

See pages 58 - 59
33
Calculating Acceleration

• The relationship of acceleration, change in
  velocity, and time interval is given by the
  equation
• Example
• A pool ball traveling at 2.5 m/s, towards the
  cushion bounces off at 1.5 m/s. If the ball was
  in contact with the cushion for 0.20 s, what is
  the balls acceleration? (Assume towards the
  cushion is the positive direction.)

See pages 60 - 61
34
Calculating Acceleration

• The relationship of change in velocity,
  acceleration, and time interval is given by the
  equation
• Example
• A car accelerates from rest at 3.0 m/s2 forward
  for 5.0 s. What is the velocity of the car at the
  end of 5.0 s?

The cars change in velocity is 15 m/s forward,
therefore
See pages 60 - 61
The cars velocity after 5.0 s is 15 m/s forward.
35
Calculating Acceleration

• The relationship of time interval, change in
  velocity, and acceleration is given by the
  equation
• Example
• A train is travelling east at 14 m/s. How long
  would to increase its velocity to 22 m/s east, if
  it accelerated at 0.50 m/s2 east? (assign east
  direction positive ()).

To find the value of Dt
See pages 60 - 61
It would take 16 s for the train to increase its
velocity.
36
Calculating Acceleration

• Try the following acceleration problems.
• Answers on the next slide.
• A truck starting from rest accelerates uniformly
  to 18 m/s W in 4.5 s. What is the trucks
  acceleration?
• A toboggan moving 5.0 m/s forward decelerates
  backwards at -0.40 m/s2 for 10 s. What is the
  toboggans velocity at the end of the 10 s?
• How much time does it take a car, travelling
  south at 12 m/s, to increase its velocity to
  26 m/s south if it accelerates at 3.5 m/s2 south?

See page 61
37
Calculating Acceleration

• Try the following acceleration problems.
• A truck starting from rest accelerates uniformly
  to 18 m/s W in 4.5 s. What is the trucks
  acceleration? (4.0 m/s2 W)
• A toboggan moving 5.0 m/s forward decelerates
  backwards at -0.40 m/s2 for 10 s. What is the
  toboggans velocity at the end of the 10 s? (1.0
  m/s forward)
• How much time does it take a car, travelling
  south at 12 m/s, to increase its velocity to
  26 m/s south if it accelerates at 3.5 m/s2 south?
  (4.0 s)

See page 61
38
Gravity and Acceleration

• Objects, near the surface of the Earth, fall to
  the Earth due to the force of gravity.
• Gravity is a pulling force that acts between two
  or more masses.
• Air resistance is a friction-like force that
  opposes the motion of objects that move through
  the air.
• Ignoring air resistance, all objects will
  accelerate towards the Earth at the same rate.
• The acceleration due to gravity is given as 9.8
  m/s2 downward.

See pages 62 - 63
39
Calculating Motion Due to Gravity

• To analyze situation where objects are
  accelerating due to gravity, use the equations
• In these equations the acceleration ( ) is 9.8
  m/s2 downward.
• Example
• Suppose a rock falls from the top of a cliff.
  What is the change in velocity of the rock after
  it has fallen for 1.5 s? (Assign down as
  negative (-))

Since down is negative (-), the change in the
rocks velocity is 15 m/s down.
See page 64
40
Calculating Motion Due to Gravity

• Try the following acceleration due to gravity
  problems. (Answers on the next slide)
• What is the change in velocity of a brick that
  falls for 3.5 s?
• A ball is thrown straight up into the air at 14
  m/s. How long does it take for the ball to slow
  down to an upward velocity of 6.0 m/s?
• A rock is thrown downwards with an initial
  velocity of 8.0 m/s. What is the velocity of the
  rock after 1.5 s?

See page 64
41
Calculating Motion Due to Gravity

• Try the following acceleration due to gravity
  problems.
• What is the change in velocity of a brick that
  falls for 3.5 s? (34 m/s downward)
• A ball is thrown straight up into the air at 14
  m/s. How long does it take for the ball to slow
  down to an upward velocity of 6.0 m/s? (0.82 s)
• A rock is thrown downwards with an initial
  velocity of 8.0 m/s. What is the velocity of the
  rock after 1.5 s? (23 m/s downward)

See page 64
Take the Section 9.2 Quiz