Kinematics in One

doutfanaticalMechanics

Nov 14, 2013 (3 years and 8 months ago)

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C H A P T E R

2

Kinematics in One
Dimension


Mechanics

The study of
Physics
begins with mechanics.


Mechanics

The study of
Physics
begins with mechanics.


Mechanics

is the branch of physics that focuses on the motion
of objects and the forces that cause the motion to change.

Mechanics

The study of
Physics
begins with mechanics.


Mechanics

is the branch of physics that focuses on the motion
of objects and the forces that cause the motion to change.

There are two parts to mechanics:
Kinematics

and
Dynamics
.

Mechanics

The study of
Physics
begins with mechanics.


Mechanics

is the branch of physics that focuses on the motion
of objects and the forces that cause the motion to change.

There are two parts to mechanics:
Kinematics

and
Dynamics
.

Kinematics

deals with the concepts that are needed to describe
motion, without any reference to forces.


Chapter 2: Kinematics in one dimension


Chapter 3: Kinematics in two dimensions

Mechanics

The study of
Physics
begins with mechanics.


Mechanics

is the branch of physics that focuses on the motion
of objects and the forces that cause the motion to change.

There are two parts to mechanics:
Kinematics

and
Dynamics
.

Kinematics

deals with the concepts that are needed to describe
motion, without any reference to forces.


Chapter 2: Kinematics in one dimension


Chapter 3: Kinematics in two dimensions

Dynamics

deals with the effect that forces have on motion.


Chapter 4: Dynamics

Distance and Displacement



Distance and Displacement



Starting from origin, O a person walks 90
-
m east, then turns
around and walks 40
-
m west.

Distance and Displacement



Starting from origin, O a person walks 90
-
m east, then turns
around and walks 40
-
m west.

Q: What is the total walked distance?

Distance and Displacement



Starting from origin, O a person walks 90
-
m east, then turns
around and walks 40
-
m west.

Q: What is the total walked distance? A: 130
-
m

Distance and Displacement



Starting from origin, O a person walks 90
-
m east, then turns
around and walks 40
-
m west.

Q: What is the total walked distance? A: 130
-
m

Q: What is the displacement?

Distance and Displacement



Starting from origin, O a person walks 90
-
m east, then turns
around and walks 40
-
m west.

Q: What is the total walked distance? A: 130
-
m

Q: What is the displacement? A: 50
-
m, due east.

Displacement



position

initial


o
x

position

final


x

nt
displaceme





o
x
x
x



The
displacement

Ä
x

is a
vector

that points from the initial position
to the final position
.
SI Unit of Displacement:

meter (m)



Figure 2
-
2

One
-
Dimensional Coordinates

2.2 Speed and Velocity


Average Speed


Average Velocity


Instantaneous Velocity


Instantaneous Speed

Average Speed

Units for speed: m/s, MPH, kmPH.

Conceptual Checkpoint 2
-
1

Average Speed

Average Velocity

t
t
t
o
o






x
x
x
v




Units for velocity: m/s, MPH, kmPH.

time
Elapsed
nt
Displaceme


velocity
Average

Figure 2
-
6

Constant Velocity on an
x
-
Versus
-
t

Graph

Example 2
-
2

Sprint Training

Figure 2
-
4

Motion Along the
X

Axis Represented with an
x
-
Versus
-
t

Graph

Figure 2
-
5a

Average Velocity on an
x
-
Versus
-
t

Graph

Figure 2
-
5b

Average Velocity on an
x
-
Versus
-
t

Graph

Instantaneous Velocity and Speed


The
instantaneous velocity

v

indicates how fast an object
moves and the direction of the motion at each instant of time.

t
t





x
v


0
lim
The magnitude of the instantaneous velocity is called the
instantaneous speed
, and it is the number (with units) indicated
by the speedometer.


Figure 2
-
7

Instantaneous Velocity

Figure 2
-
8

Graphical Interpretation of Average and Instantaneous Velocity

Acceleration

Acceleration

Units: m/s
2
, cm/s
2


Table 2
-
3

Typical Accelerations (m/s
2
)

Ultracentrifuge

3 x 10
6

Batted baseball

3 x 10
4

Bungee jump

30

Acceleration of gravity on Earth

9.81

Emergency stop in a car

8

Acceleration of gravity on the Moon

1.62

Figure 2
-
9

v
-
Versus
-
t

Plots for Motion with Constant Acceleration

Example 2
-
3

An Accelerating Train

Instantaneous acceleration


Acceleration at a particular instant is called instantaneous
acceleration.

Figure 2
-
10

Graphical Interpretation of Average and Instantaneous Acceleration

Deceleration

Deceleration

An object speeds up when the acceleration and velocity vectors
point in the same direction.

Deceleration

An object speeds up when the acceleration and velocity vectors
point in the same direction.

Whenever the acceleration and velocity vectors have opposite
directions, the object slows down and is said to be “decelerating.”

Figure 2
-
11

Cars Accelerating or Decelerating

Deceleration

An object speeds up when the acceleration and velocity vectors
point in the same direction.

Whenever the acceleration and velocity vectors have opposite
directions, the object slows down and is said to be “decelerating.”

Example 4: A drag racer crosses the finish line, and the driver
deploys a parachute and applies the brakes to slow down. The
driver begins slowing down when
t
0

= 9.0 s and the car's
velocity

is
v
0

= +28 m/s. When
t

= 12.0 s, the velocity has been reduced to
v

= +13 m/s. What is the average
acceleration

of the dragster?

Kinematics Equations

Figure 2
-
13a

The Average Velocity

Figure 2
-
14

Velocity Versus Time for the Boat in Example 2
-
5