Motion in

1
Motion in One Dimension
2
Motion in One Dimension
Sections
2-01 Displacement
2-02 Velocity
2-03 Acceleration
2-04 Motion Diagrams
2-05 One Dimensional Motion with
Constant Acceleration
2-06 Freely Falling Objects
3
Displacement
v
In the study of kinematics, we consider a moving
object as a particle.
A particle is a point-like mass having
infinitesimal size and a finite
mass. Kinematics is a part of dynamics In
kinematics, you are interested in the description
of motion Not concerned with the cause of the
motion
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Displacement
The displacement of a particle is defined as its
change in position.
x
(m)
0
2
4
6
-2
-4
-6
Dx x - xo 6 m - 2 m 4 m
Note Displacement to the right is positive
5
Displacement
The displacement of a particle is defined as its
change in position.
x
(m)
0
2
4
6
-2
-4
-6
Dx x - xo -6 m - 6 m -12 m
Note Displacement to the left is negative
6
Displacement
The displacement of a particle is defined as its
change in position.
x
(m)
0
2
4
6
-2
-4
-6
Dx x - xo (2 m) - (-6 m) 8 m
Note Displacement to the right is positive
7
Displacement

• Defined as the change in position
• f stands for final and i stands for initial
• May be represented as ?y if vertical
• Units are meters (m) in SI, centimeters (cm) in
  cgs or feet (ft) in US Customary

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Displacement
A student walks 70 m East, then walks 30 km
West. What is the magnitude of the students net
displacement? A) 30 m B) 40 m C) 70 m D) 100 m
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Velocity
Average velocity
The average velocity of a particle is
defined as
x
Velocity is represented by the slope on a
displacement-time graph
t
10
Velocity
Average speed
The average speed of a particle is defined as
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Velocity
Instantaneous velocity
The instantaneous velocity v, equals the limiting
value of the ratio
Instantaneous velocity is represented by the
slope of a displacement-time graph
Instantaneous speed
The instantaneous speed of a particle is defined
as the magnitude of its instantaneous velocity.
12
Sample Problems
http//dev.physicslab.org/Document.aspx?doctype5
filenameKinematics_AverageSpeedAverageVelocity.xm
l
Graphing Notes before Next Page
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Motion Diagrams
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Motion Diagrams
The displacement versus time for a certain
particle moving along the x axis is shown below.
Find the average velocity in the time intervals
(a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d)
4 s to 7 s (e) 0 to 8 s.
15
Motion Diagrams (cont)
The displacement versus time for a certain
particle moving along the x axis is shown below.
Find the average velocity in the time intervals
(a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d)
4 s to 7 s (e) 0 to 8 s.
16
Motion Diagrams (cont)
The displacement versus time for a certain
particle moving along the x axis is shown below.
Find the average velocity in the time intervals
(a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d)
4 s to 7 s (e) 0 to 8 s.
17
Motion Diagrams (cont)
The displacement versus time for a certain
particle moving along the x axis is shown below.
Find the average velocity in the time intervals
(a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d)
4 s to 7 s (e) 0 to 8 s.
18
Motion Diagrams (cont)
The displacement versus time for a certain
particle moving along the x axis is shown below.
Find the average velocity in the time intervals
(a) 0 to 2 s (b) 0 to 4 s (c) 2 s to 4 s (d)
4 s to 7 s (e) 0 to 8 s.
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Acceleration
Average acceleration
The average acceleration of a particle is defined
as the change in velocity Dvx divided by the
time interval Dt during which that change
occurred.
v
Acceleration is represented by the slope on a
velocity-time graph
t
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Acceleration
A new car manufacturer advertises that their car
can go "from zero to sixty in 8 s". This is a
description of A) instantaneous acceleration. B)
average speed. C) instantaneous speed. D)
average acceleration.
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Acceleration
A moving car experiences a constant acceleration
of 1.5 m/s2. This means the car is A) traveling
at 1.5 m/s in every second. B) changing its
velocity by 1.5 m/s. C) increasing its velocity
by 1.5 m/s in every second. D) increases its
displacement by 1.50 m each second.
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Quick Quiz 2.2
True or False? (a) A car must always have an
acceleration in the same direction as its
velocity
False
(b) Its possible for a slowing car to have
a positive acceleration
True
(c) An object with constant nonzero acceleration
can never stop and stay stopped.
True
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Sample Problem (HP book)