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7/24/2019 kinematics 1.1.pdf
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Raymond A. Serway
Chris Vuille
Chapter Two
Motion in One Dimension
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Kinematics definitions
Kinematicsbranch of physics; study of
motion
Position (x)where you are located
Distance (d)how far you have traveled,
regardless of direction
Displacement (x)where you are inrelation to where you started
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Dynamics
The branch of physics involving the motion ofan object and the relationship between thatmotion and other physics concepts
Kinematicsis a part of dynamics In kinematics, you are interested in the description
of motion
Notconcerned with the cause of the motion
Introduction
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Displacement
positioninitialox
positionfinalx
ntdisplacemeo
xxx
The displacementxis a vectorthat points from the initial position to the final
position. SI Unit of Displacement:meter (m)
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Distance vs. Displacement
You drive the path, and your odometer goes up by 8miles (your distance).
Your displacement is the shorter directed distance
from start to stop (green arrow). What if you drove in a circle?
start
stop
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Distance
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Speed, Velocity, & Acceleration
Speed (v)how fast you go
Velocity (v)how fast and which way;
the rate at which position changes Average speed ( v)distance/time
Acceleration (
a
)how fast you speedup, slow down, or change direction;the rate at which velocity changes
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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
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Displacement Examples
From A to B xi= 30 m
xf= 52 m
x = 22 m
The displacement is positive, indicating the motionwas in the positive x direction
From C to F xi= 38 m xf= -53 m
x = -91 m
The displacement is negative,
indicating the motion was in
the negative x direction Section 2.1
i l
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Displacement,
Graphical
Section 2.1
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Average Velocity
ttto
o
xxx
v
Units for velocity: m/s, MPH, kmPH.
timeElapsed
ntDisplacemevelocityAverage
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(x0, t0)
(x2, t2)
(x1, t1)
(x5, t5)
(x4, t4)
(x3, t3)
(x6, t6)
point x (m) t (s)
O 0 0
A 1 1
B 5 2C 12 3
D 8 4
E 10 5
F 5 6
A
0
B
CE
D
F
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i t ( ) t ( )
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point x (m) t (s)
O 0 0
A 1 1
B 5 2
C 12 3
D 8 4
E 10 5
F 5 6
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the specific features of the motion of
objects are demonstrated by the shape and
the slope of the lines on a position vs. timegraph.
To begin, consider a car moving with a constant, rightward
(+) velocity- say of +10 m/s.
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Now consider a car moving with a rightward (+),
changing velocity- that is, a car that is moving
rightward but speeding up or accelerating.
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Constant Velocity
Positive Velocity
Positive Velocity
Changing Velocity (acceleration)
Slow, Rightward(+)
Constant Velocity
Fast, Rightward(+)
Constant Velocity
Slow, Leftward(-)
Constant Velocity Fast, Leftward(-)Constant Velocity
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AccelerationAccelerationhow fast you speed up, slow
down, or change direction; its the rate atwhich velocity changes.
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Negative Acceleration
A negative acceleration does not necessarily
mean the object is slowing down
If the acceleration and velocity are both
negative, the object is speeding up
Deceleration means a decrease in speed,
not a negative acceleration
Section 2.3
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Velocity & Acceleration Sign Chart
V E L O C I T Y
A
C
C
EL
E
R
A
T
I
O
N
+ -
+ Moving forward;Speeding up
Moving backward;
Slowing down
- Moving forward;Slowing down
Moving backward;
Speeding up
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Acceleration due to Gravity
9.8 m/s2
Near the surface of the
Earth, all objectsaccelerate at the same
rate (ignoring air
resistance).
a= g= -9.8 m/s2
Interpretation: Velocity decreases by 9.8 m/s each second,
meaning velocity is becoming less positive or more
negative. Less positive means slowing down while going
up. More negative means speeding up while going down.
This acceleration
vector is the
same on the way
up, at the top,
and on the way
down!
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Kinematics Formula SummaryFor 1-D motion with constantacceleration:
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Motion Diagram Summary
Section 2.4
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Free Fall
A freely falling object is any object moving freely
under the influence of gravity alone
Free fall does not depend on the objects original motion
All objects falling near the earths surface fall with aconstant acceleration
The acceleration is called the acceleration due to
gravity, and indicated by g
Section 2.6
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Acceleration due to Gravity
Symbolized by g
g= 9.80 m/s
When estimating, use g 10 m/s2
gis always directed downward Toward the center of the earth
Ignoring air resistance and assuming gdoesnt varywith altitude over short vertical distances, free fall is
constantly accelerated motion
Section 2.6
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Combination Motions
Section 2.6
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In 1865 Jules Verne proposed sending men to theMoon by firing a space capsule from a 220-m-long
cannon with final speed of 10.97 km/s.
What would have been the unrealistically large
acceleration experienced by the space travelers duringtheir launch?
How much time did it took for the capsule to go from
rest to 10.97 km/s
#28 p.51 =
2 =
2
=10,970/ 0
2(220) = 273502 /
= 10,970 /
= 0 /
= 220
=
=
=
=10,970/
273,502/= 0.04
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A truck covers 40.0 m in 8.50 s
while uniformly slowing down to a
final velocity of 2.80 m/s. (a) Find the trucks original speed.
(b) Find its acceleration.
#29 p.51
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A Cessna aircraft has a liftoff
speed of 120 km/h.
(a) What minimum constantacceleration does the aircraft
require if it is to be airborne after
a takeoff run of 240 m? (b) How long does it take the
aircraft to become airborne?
#31 p.52
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In a test run, a certain car
accelerates uniformly from zero to
24.0 m/s in 2.95 s. (a) What is the magnitude of the
cars acceleration?
(b) How long does it take the car tochange its speed from 10.0 m/s to
20.0 m/s?
#33 p.52
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A train is traveling down a straight
track at 20 m/s when the engineer
applies the brakes, resulting in anacceleration of -1.0 m/s2as long
as the train is in motion.
How far does the train moveduring a 40-s time interval
starting at the instant the brakes
are applied?
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A ball is thrown vertically upwardwith a speed of 25.0 m/s.
(a) How high does it rise?
(b) How long does it take to reachits highest point?
(c) How long does the ball take tohit the ground after it reaches itshighest point?
(d) What is its velocity when it
returns to the level from which itstarted?
#45 p.52
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A baseball is hit so that it travels
straight upward after being struck
by the bat. A fan observes that ittakes 3.00 s for the ball to reach
its maximum height.
Find (a) the balls initial velocityand
(b) the height it reaches.
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