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2 Kinematics• distance, location, displacement
• speed, velocity, acceleration
• free fall
• Homework:
• 7, 8, 11, 31, 33, 41, 45, 65, 70, 88, 100, 101.
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Applications
• Destination times
• Design packing materials & road barriers
• Airbag deployment speed
• Simulations (movies & games)
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Speed
• Speed = rate of travel at a given moment of time
• Distance traveled = total length of the curved path
[m/s] timeelapsed
traveleddistancespeed avg.
Initial/Final Notation
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0 tat timeposition ox
t at timeposition x
Same rules apply for all variables
Delta Notation
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quantity of in value change means
oxxx
ovvv
0) choosen often is ( oo tttt
called Displacement
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Acceleration (m/s/s)
t
vaavg
:onaccelerati average
If t is small, v/t is called the instantaneous acceleration and labeled “a”.
Ex. Car Acceleration
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from 10m/s to 15m/s in a time of 2.0 seconds.
m/s/s 5.20.0s-2.0
10m/s-15
t
vaavg
In this class we only use average acceleration and often drop the “avg” notation from acceleration.
Average Velocity with Uniform Acceleration
• Uniform Acceleration = constant valued acceleration
• During uniform acceleration, average velocity is halfway between vo and v:
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2
vvv oavg
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Kinematic Equations with Constant Acceleration
atvv o :velocity
tvvx o )( : velocityaverage 21
221 :ntdisplaceme attvx o
xavv o 2 :squared-v 22
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Ex. Human Acceleration
mat 20221
In the 1988 Olympics, Carl Lewis reached the 20m mark in 2.96s (Bolt: 2.87s)
20)96.2( 221 a
ssms
ma //56.4
)96.2(
2022
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Ex: V2 EquationApproximate Stopping Accelerations in m/s/s:
Dry Road: ~ 9 (anti-lock) ~ 7 (skidding)
Wet Road: ~ 4 (anti-lock) ~ 2 (skidding)
At 60mph = 27m/s, what is the skid-to-stop distance on a wet road?
feet) 006(about 182
)2(2270
222
22
mx
x
xavv o
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Scalars & Vectors• Scalar: size only
• e.g. speed, distance, time
• Vector: magnitude and direction
• e.g. displacement, velocity, acceleration
• In one-dimension the direction is determined by the + or – sign.
• In two-dimensions, two numbers are required.
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Motion Diagrams
• Are velocity-position diagrams• More visual than a graph of x or v vs. time• Arrow gives direction, length represents the speed
(use a dot for zero speed)• (net) force required to change velocity• Example: car speeding up to left
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Free-Fall Acceleration
• a = 9.8m/s/s in downward direction
• Ex. Speed of object dropped from rest after 1.0, 2.0, 3.0 seconds:
• v = vo + at
• v(1.0s) = 0 + (-9.8)(1.0) = -9.8m/s
• v(2.0s) = 0 + (-9.8)(2.0) = -19.6m/s
• v(3.0s) = 0 + (-9.8)(3.0) = -29.4m/s
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