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Unformatted text preview: ∆x ) 3 = 100 m + 400 m + 50 m =550 m
and the average velocity for the total motion is given by v= 2.31 ∆x 550 m
=
= 16 m s .
t total
35 s ( ) 1
1
(a) Using ∆x = v i t + at 2 with v i = 0 gives 400 m = 0 + 10.0 m s 2 t 2 , yielding
2
2
t = 8.94 s . ( ) (b) From v f = v i + at , with v i = 0 , we find v f = 0 + 10.0 m s 2 ( 8.94 s ) = 89.4 m s . 30 CHAPTER 2.32 (a) The time required to stop is t = v f − vi
a = 2 0 − 100 m s
= 20.0 s .
− 5.00 m s 2 (b) The minimum distance needed to stop the plane is
⎛ v f + v i ⎞ ⎛ 0 + 100 m s ⎞
t =⎜
∆x = v t = ⎜
⎟ ( 20.0 s ) = 1000 m = 1.00 k m .
⎠
2
⎝2⎟⎝
⎠ Thus, the plane cannot stop in 0.8 km.
2.33 Using v 2 = v i2 + 2 a( ∆x ) , with v f = 0 and v i = 60 m i h , yields
f ⎡0 − ( 60 m i h ) 2 ⎤
⎦ ⎛ 0.447 m
a=
=⎣
⎜ 1 mi h
2 ( ∆x )
2 (100 m )
⎝
v 2 − v i2
f 2.34 2 s⎞
2
⎟ = − 3.6 m s .
⎠ The velocity at the end of the first interval is v f = v i + at = 0 + (2 .77 m s) (15.0 s ) = 41.6 m s .
This is also the constant velocity during the second interval and the initial velocity for
the third interval. 1
(a) From ∆x = v i t + at 2 , the total displacement is
2 ∆x = ( ∆x )1 + ( ∆x ) 2 + ( ∆x ) 3
1
2⎤
⎡
= ⎢0 + 2 .77 m s 2 (15.0 s ) ⎥ + ⎡( 41.6 m s ) (123 s ) + 0 ⎤
⎦
2
⎣
⎦⎣
1
2⎤
⎡
+ ⎢( 41.6 m s ) ( 4.39 s ) + − 9.47 m s 2 ( 4.39 s ) ⎥
2
⎣
⎦ ( ) ( ) or ∆x = 312 m + 5.11 × 103 m + 91.2 m = 5.51 × 103 m = 5.51 k m 31 CHAPTER (b) v 1 = v2 = v3 = ( ∆x )1 312 m
t1 ( ∆x ) 2
t2 ( ∆x ) 3
t3 = 15.0 s = 20.8 m s , = 5.11 × 103 m
= 41.6 m s ,
123 s = 91.2 m
= 20.8 m s , and the average velocity for the
4.39 s total trip is v total = 2.35 2 ∆x
5.51 × 103 m
=
= 38.7 m s
t total (15.0+123+4.39) s 1
Using the uniformly accelerated motion equation ∆x = v i t + at 2 for the full 40 s interval
2
1
2
yields ∆x = ( 20 m s ) ( 40 s ) + −1.0 m s 2 ( 40 s ) = 0 , which is obviously wrong.
2 ( ) The source of the error is found by computing the time required for the train to come to
v f − v i 0 − 20 m s
rest. T...
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This note was uploaded on 03/03/2010 for the course PHY P221 taught by Professor Dr.ha during the Spring '05 term at Indiana University South Bend.
 Spring '05
 Dr.Ha
 Physics, Acceleration

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