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Eunil Won Dept. of Physics, Korea University 2
Displacement
position: x
1x 2x
displacement 12 xxx −≡∆
Eunil Won Dept. of Physics, Korea University 4
Average speed, instantaneous speed
tx
ttxxv
∆∆=
−−≡
12
12
dtdx
ttxttxv
t=
∆−∆+≡
∞→∆
)()(lim
Eunil Won Dept. of Physics, Korea University 5
Acceleration
2
2
limdt
xddtdx
dtd
dtdv
tva
t=⎟
⎠⎞
⎜⎝⎛==
∆∆≡
∞→∆
Eunil Won Dept. of Physics, Korea University 7
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
Eunil Won Dept. of Physics, Korea University 8
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
Eunil Won Dept. of Physics, Korea University 9
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?
Eunil Won Dept. of Physics, Korea University 10
Constant accelerating motion
.consdtdva ==
∫ ∫ ∫== dtaadtdv
dtdxv =
∫ ∫ ∫ +== dtatvvdtdx )( 0
221
00 attvxx ++=
atvv += 0
Eunil Won Dept. of Physics, Korea University 12
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
Eunil Won Dept. of Physics, Korea University 13
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.
Eunil Won Dept. of Physics, Korea University 14
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