Eunil Won Dept. of Physics, Korea University 1

Ch02 Motion

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Displacement

position: x

1x 2x

displacement 12 xxx −≡∆

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Average speed, instantaneous speed

tx

ttxxv

∆∆=

−−≡

12

12

dtdx

ttxttxv

t=

∆−∆+≡

∞→∆

)()(lim

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Acceleration

2

2

limdt

xddtdx

dtd

dtdv

tva

t=⎟

⎠⎞

⎜⎝⎛==

∆∆≡

∞→∆

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Examples 2.1/2.2/2.3

Eastminkm40.0

min15East km0.6 ==v Eastkm/h 24

hmin60

minkm40.0 =×=v

Westsh

km0.6Wests15

km/h 90⋅

==∆∆=

tva

Westm/s67.1km1

m10s3600

h1sh

km0.6 23

=××⋅

=a

38smin 4s1078.2m/s4.5

m1500 2 ⇒×===vlt

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Examples 2.4/2.5/2.6

20

m/s08

m/s00

.avt

=

==

?s75.0

==

vt constant=v

20

m/s2

??

−=

==

avt

velocity

Time elapsed

Distance run

m/s0.6)75.0)(0.8(00 =+=+= atvv

s0.32

0.600 =−−=−=

avvt

m0.9)0.3)(0.2()0.3)(0.6( 2212

21

0 =−+=+= attvs

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Example 2.7

24

20

2

m/s1028.1)400)(16(20

2

×=+=

+= asvv

A constant accelerating vehicle (a=16 m/s2) is started from rest. What is the instantaneous velocity after traveling 400 m?

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Constant accelerating motion

.consdtdva ==

∫ ∫ ∫== dtaadtdv

dtdxv =

∫ ∫ ∫ +== dtatvvdtdx )( 0

221

00 attvxx ++=

atvv += 0

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Acceleration of gravity2m/s8.9−=g

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Example 2.8

m/s100 =v

m10.5)8.9(2)10(0

2

222

02

20

2

=−

−=−=

+=

avvs

asvv

Distance traveled upward

Time elapsed

s02.18.9

1000 =−−=−=

avvt

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Example 2.9

s50.38.9

)0.60(2

2

0

2/1

2212

21

0

=⎥⎦⎤

⎢⎣⎡

−−=

=

+=+=

ast

atattvs

m1.44)0.3)(8.9(

m6.19)0.2)(8.9(

m9.4)0.1)(8.9(

0

2212

321

3

2212

221

2

2212

121

1

2212

21

0

−=−==

−=−==

−=−==

+=+=

ats

ats

ats

atattvs

A rock is dropped into a 60.0 m deep well.

(a) How long will it take the rock to reach bottom?

(b) Calculate the position of the rock 1.0, 2.0, and 3.0 sec after its release.

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Example 2.10

2

2

20

m/s7.34

)50)(8.9(2)15(

2

−=

−−++=

+= asvv

2

2

20

m/s7.34

)50)(8.9(2)15(

2

−=

−−+−=

+= asvv

A youngster throws a rock from a bridge into the river 50m below. The rock has a speed of 15 m/s when it leaves the youngster. Calculated the velocity of the rock when it strikes the water (a) if it is thrown straight upward, (b) if it is thrown straight downward