77 m s 150 s 416 m s this is also the constant

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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.

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