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Kinematics in One Dimension

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Title: Kinematics in One Dimension


1
Kinematics in One Dimension
Chapter 2
2
Kinematics deals with the concepts that are
needed to describe motion. Dynamics deals with
the effect that forces have on motion. Together,
kinematics and dynamics form the branch of
physics known as Mechanics.
3
  • Scalars are quantities which are fully described
    by a magnitude alone. (think of how much)
  • Vectors are quantities which are fully described
    by both a magnitude and a direction. (think of
    which way direction)
  • Check your understanding..
  • 5 m
  • 30 m/sec, East
  • 5 mi., North
  • 20 degrees Celsius
  • 256 bytes
  • 4000 Calories

4
Lesson 1 Describing Motion with
WordsIntroduction to the Language of Kinematics
  • Distance is a scalar quantity which refers to
    "how much ground an object has covered" during
    its motion.
  • Displacement is a vector quantity which refers to
    "how far out of place an object is" it is the
    object's change in position.

5
2.1 Displacement
6
Lesson 1 Describing Motion with
WordsIntroduction to the Language of Kinematics
  • Distance is a scalar quantity which refers to
    "how much ground an object has covered" during
    its motion.
  • Displacement is a vector quantity which refers to
    "how far out of place an object is" it is the
    object's change in position.

7
2.1 Displacement
8
2.1 Displacement
9
2.1 Displacement
10
Lesson 1 Describing Motion with WordsSpeed and
Velocity
  • Speed is a scalar quantity which refers to "how
    fast an object is moving." A fast-moving object
    has a high speed while a slow-moving object has a
    low speed. An object with no movement at all has
    a zero speed.
  • Velocity is a vector quantity which refers to
    "the rate at which an object changes its
    position."

11
2.2 Speed and Velocity
Average speed is the distance traveled divided by
the time required to cover the distance.
SI units for speed meters per second (m/s)
12
2.2 Speed and Velocity
Example 1 Distance Run by a Jogger How far does
a jogger run in 1.5 hours if his average speed
is 2.22 m/s?
13
2.2 Speed and Velocity
Average velocity is the displacement divided by
the elapsed time.
14
2.2 Speed and Velocity
Example 2 The Worlds Fastest Jet-Engine
Car Andy Green in the car ThrustSSC set a world
record of 341.1 m/s in 1997. To establish such
a record, the driver makes two runs through the
course, one in each direction, to nullify wind
effects. From the data, determine the
average velocity for each run.
15
2.2 Speed and Velocity
16
Constant Speed problems
A horse canters away from its trainer in a
straight line moving 100. m away in 16.0 s. It
then turns abruptly and gallops halfway back in
4.6. Calculate the average speed and average
velocity. A bike travels at a constant speed of
4.0 m/s for 5 s. How far does it go? The round
trip distance between Earth and the moon is
350,000 km, if the speed of a laser is 3.0 x 108
m/s how much time does it take the laser to
travel from Earth to the moon?
17
2.3 Acceleration
The notion of acceleration emerges when a change
in velocity is combined with the time during
which the change occurs.
18
2.3 Acceleration
DEFINITION OF AVERAGE ACCELERATION
19
2.3 Acceleration
Example 3 Acceleration and Increasing
Velocity Determine the average acceleration of
the plane.
20
2.3 Acceleration
21
2.3 Acceleration
Example 3 Acceleration and Decreasing Velocity
22
2.4 Equations of Kinematics for Constant
Acceleration
Equations of Kinematics for Constant Acceleration
23
2.4 Equations of Kinematics for Constant
Acceleration
Five kinematic variables 1. displacement, x 2.
acceleration (constant), a 3. final velocity (at
time t), v 4. initial velocity, vo 5. elapsed
time, t
24
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25
2.4 Equations of Kinematics for Constant
Acceleration
26
2.4 Equations of Kinematics for Constant
Acceleration
Example 6 Catapulting a Jet Find its
displacement.
27
2.4 Equations of Kinematics for Constant
Acceleration
28
2.5 Applications of the Equations of Kinematics
Reasoning Strategy 1. Make a drawing. 2. Decide
which directions are to be called positive ()
and negative (-). 3. Write down the values
that are given for any of the five kinematic
variables. 4. Verify that the information
contains values for at least three of the five
kinematic variables. Select the appropriate
equation. 5. When the motion is divided into
segments, remember that the final velocity of one
segment is the initial velocity for the next. 6.
Keep in mind that there may be two possible
answers to a kinematics problem.
29
2.5 Applications of the Equations of Kinematics
Example 8 An Accelerating Spacecraft A
spacecraft is traveling with a velocity of 3250
m/s. Suddenly the retrorockets are fired, and
the spacecraft begins to slow down with an
acceleration whose magnitude is 10.0 m/s2. What
is the velocity of the spacecraft when the
displacement of the craft is 215 km, relative to
the point where the retrorockets began firing?
x a v vo t
215000 m -10.0 m/s2 ? 3250 m/s
30
2.5 Applications of the Equations of Kinematics
x a v vo t
215000 m -10.0 m/s2 ? 3250 m/s
31
2.6 Freely Falling Bodies
In the absence of air resistance, it is found
that all bodies at the same location above the
Earth fall vertically with the same
acceleration.
This idealized motion is called free-fall and the
acceleration of a freely falling body is called
the acceleration due to gravity.
32
2.6 Freely Falling Bodies
33
2.6 Freely Falling Bodies
Example 10 A Falling Stone A stone is dropped
from the top of a tall building. After 3.00s of
free fall, what is the displacement y of the
stone?
34
2.6 Freely Falling Bodies
y a v vo t
? -9.80 m/s2 0 m/s 3.00 s
35
2.6 Freely Falling Bodies
y a v vo t
? -9.80 m/s2 0 m/s 3.00 s
36
2.6 Freely Falling Bodies
Example 12 How High Does it Go? The referee
tosses the coin up with an initial speed of
5.00m/s. In the absence if air resistance, how
high does the coin go above its point of release?
37
2.6 Freely Falling Bodies
y a v vo t
? -9.80 m/s2 0 m/s 5.00 m/s
38
2.6 Freely Falling Bodies
y a v vo t
? -9.80 m/s2 0 m/s 5.00 m/s
39
2.6 Freely Falling Bodies
Conceptual Example 14 Acceleration Versus
Velocity There are three parts to the motion of
the coin. On the way up, the coin has a vector
velocity that is directed upward and has
decreasing magnitude. At the top of its path, the
coin momentarily has zero velocity. On the way
down, the coin has downward-pointing velocity
with an increasing magnitude. In the absence of
air resistance, does the acceleration of
the coin, like the velocity, change from one part
to another?
40
2.6 Freely Falling Bodies
Conceptual Example 15 Taking Advantage of
Symmetry Does the pellet in part b strike the
ground beneath the cliff with a smaller, greater,
or the same speed as the pellet in part a?
41
Position-Time Graphs
  • We can use a postion-time graph to illustrate the
    motion of an object.
  • Postion is on the y-axis
  • Time is on the x-axis

42
Plotting a Distance-Time Graph
  • Axis
  • Distance (position) on y-axis (vertical)
  • Time on x-axis (horizontal)
  • Slope is the velocity
  • Steeper slope faster
  • No slope (horizontal line) staying still

43
Where and When
  • We can use a position time graph to tell us where
    an object is at any moment in time.
  • Where was the car at 4 s?
  • 30 m
  • How long did it take the car to travel 20 m?
  • 3.2 s

44
Interpret this graph
45
Describing in Words
46
Describing in Words
  • Describe the motion of the object.
  • When is the object moving in the positive
    direction?
  • Negative direction.
  • When is the object stopped?
  • When is the object moving the fastest?
  • The slowest?

47
Accelerated Motion
  • In a position/displacement time graph a straight
    line denotes constant velocity.
  • In a position/displacement time graph a curved
    line denotes changing velocity (acceleration).
  • The instantaneous velocity is a line tangent to
    the curve.

48
Accelerated Motion
  • In a velocity time graph a line with no slope
    means constant velocity and no acceleration.
  • In a velocity time graph a sloping line means a
    changing velocity and the object is accelerating.

49
Velocity
  • Velocity changes when an object
  • Speeds Up
  • Slows Down
  • Change direction

50
Velocity-Time Graphs
  • Velocity is placed on the vertical or y-axis.
  • Time is place on the horizontal or x-axis.
  • We can interpret the motion of an object using a
    velocity-time graph.

51
Constant Velocity
  • Objects with a constant velocity have no
    acceleration
  • This is graphed as a flat line on a velocity time
    graph.

52
Changing Velocity
  • Objects with a changing velocity are undergoing
    acceleration.
  • Acceleration is represented on a velocity time
    graph as a sloped line.

53
Positive and Negative Velocity
  • The first set of graphs show an object traveling
    in a positive direction.
  • The second set of graphs show an object traveling
    in a negative direction.

54
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55
Speeding Up and Slowing Down
  • The graphs on the left represent an object
    speeding up.
  • The graphs on the right represent an object that
    is slowing down.

56
Two Stage Rocket
  • Between which time does the rocket have the
    greatest acceleration?
  • At which point does the velocity of the rocket
    change.

57
Displacement from a Velocity-Time Graph
  • The shaded region under a velocity time graph
    represents the displacement of the object.
  • The method used to find the area under a line on
    a velocity-time graph depends on whether the
    section bounded by the line and the axes is a
    rectangle, a triangle

58
2.7 Graphical Analysis of Velocity and
Acceleration
59
2.7 Graphical Analysis of Velocity and
Acceleration
60
2.7 Graphical Analysis of Velocity and
Acceleration
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