Physics 101Chapter 02

7/24/2019 Physics 101Chapter 02

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Chapter 2

Motion in One Dimension


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Kinematics Describes motion while ignoring

the agents that caused the motion For now, will consider motion in

one dimension Along a straight line

Will use the particle model A particle is a point-like obect, has

mass but in!nitesimal si"e


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#osition De!ned in terms o$

a frame ofreference One dimensional, so

generall% the &- or%-a&is

'he obect(s

position is itslocation withrespect to the$rame o$ re$erence


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#osition-'ime )raph 'he position-time

graph shows the

motion o$ theparticle *car+

'he smooth cureis a guess as to

what happenedbetween the datapoints


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Displacement De!ned as the change in position

during some time interal epresented as x

x .xf-xi /0 units are meters *m+ xcan be

positie or negatie Di1erent than distance the length

o$ a path $ollowed b% a particle


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Aerage /peed /peed is a scalar 4uantit%

same units as elocit%

total distance 6 total time

'he aerage speed is not*necessaril%+ the magnitude o$ the

aerage elocit%


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0nstantaneous 3elocit%'he limit o$ the aerage elocit% as

the time interal becomes

in!nitesimall% short, or as the timeinteral approaches "ero

'he instantaneous elocit%

indicates what is happening ateer% point o$ time


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0nstantaneous 3elocit%,

e4uations'he general e4uation $or

instantaneous elocit% is

'he instantaneous elocit% can bepositie, negatie, or "ero

0limx

t

x dxv

t dt

= =


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0nstantaneous 3elocit%,

graph 'he instantaneous

elocit% is the slopeo$ the line tangentto thexs: tcure

'his would be thegreen line

'he blue lines showthat as tgetssmaller, the%approach the greenline


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0nstantaneous /peed'he instantaneous speed is the

magnitude o$ the instantaneous

elocit% emember that the aerage speed

is not the magnitude o$ the

aerage elocit%


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Aerage Acceleration Acceleration is the rate o$ change

o$ the elocit%

Dimensions are 86'2

/0 units are m6s;

xf xixx

v vva

t t

= =


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0nstantaneous

Acceleration'he instantaneous acceleration is

the limit o$ the aerage

acceleration as tapproaches

3elocit% and acceleration are in the same direction

Acceleration is uni$orm *blue arrows maintain thesame length+ 3elocit% is increasing *red arrows are getting longer+ 'his shows positie acceleration and positie elocit%


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Acceleration and 3elocit%,

?

Acceleration and elocit% are in opposite directions

Acceleration is uni$orm *blue arrows maintain thesame length+ 3elocit% is decreasing *red arrows are getting shorter+ #ositie elocit% and negatie acceleration


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Kinematic @4uations,

speci!c For constant acceleration,

'his gies %ou the position o$ the

particle in terms o$ time andelocities

Doesn(t gie %ou the acceleration

() 12

fiixifx xxvtxvvt =+=++


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speci!c For constant acceleration,

)ies !nal position in terms o$elocit% and acceleration

Doesn(t tell %ou about !nal elocit%

212

f i xi xx x v t a t= + +


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speci!c For constant a,

)ies !nal elocit% in terms o$

acceleration and displacement

Does not gie an% in$ormationabout the time

() 222xfxixfi

vvaxx =+


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)raphical 8ook at Motion

displacement time cure 'he slope o$ the

cure is the

elocit% 'he cured line

indicates theelocit% is

changing 'here$ore, there is

an acceleration


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Acceleration o$ Freel%

Falling Obect 'he acceleration o$ an obect in $ree $all

is directed downward, regardless o$ the

initial motion 'he magnitude o$ $ree $all acceleration

is g. :< m6s2

gdecreases with increasing altitude

garies with latitude

:< m6s2is the aerage at the @arth(ssur$ace


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Acceleration o$ Free Fall,

cont: We will neglect air resistance

Free $all motion is constantl%

accelerated motion in onedimension

8et upward be positie

Ese the kinematic e4uations withay. g. -:< m6s2


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Free Fall @&ample 0nitial elocit% at A is upward *5+

and acceleration is g*-: m6s2+

At , the elocit% is < and theacceleration is g*-: m6s2+

At C, the elocit% has the samemagnitude as at A, but is in theopposite direction

'he displacement is G


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Motion @4uations $rom

Calculus Displacement

e4uals the area

under the elocit% time cure

'he limit o$ thesum is a de!niteintegral

0

lim ( )f

in

t

xn n xtt

n

v t v t dt

=


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Kinematic @4uations Calculus Form with

Constant Acceleration

'he integration $orm o$ vf vigies

'he integration $orm o$xfxigies

xf xi xv v a t =

21

2f i xi xx x v t a t = +


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)eneral #roblem /oling

/trateg% Conceptuali"e

Categori"e

Anal%"e

Finali"e


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#roblem /oling

Categori"e /impli$% the problem

Can %ou ignore air resistanceH

Model obects as particles

Classi$% the t%pe o$ problem

'r% to identi$% similar problems %ou

hae alread% soled


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#roblem /oling Anal%"e /elect the releant e4uation*s+ to

appl%

/ole $or the unknown ariable /ubstitute appropriate numbers

Calculate the results

0nclude units ound the result to the appropriate

number o$ signi!cant !gures


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#roblem /oling Finali"e Check %our result

Does it hae the correct unitsH

Does it agree with %ourconceptuali"ed ideasH

8ook at limiting situations to besure the results are reasonable

Compare the result with those o$similar problems


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Physics 101Chapter 02