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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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Velocity (m/s)

t

xvavg

: velocityaverage

When t is small, x/t is the instantaneous velocity v.

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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.

Velocity Formula

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tvaavg /

tav

tavv o

atvv o

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

Average Velocity Formula

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t

xvavg

tvx avg

tvvx )( 021

Displacement Formula

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tvvx o )(21

tatvvx oo }){(21

tatvx o )2(21

221 attvx o

V-squared Equation

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atvv o avvt o /)(

avvvvx o /))(( 021

tvvx )( 021

avvx o /)( 2221

xavv o 222

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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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Activities

• Moving Man phet animae

• Textbook type problems

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Summary:• speed: rate of travel• average speed: distance traveled/time.• displacement: change in position• velocity: rate position changes• acceleration: rate velocity changes• kinematic equation set (p.46)• free fall: constant acceleration.• graphs and slopes