0 m i h 147 ft s 160 ft 2 331 ft s 2 1 m i h 2

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Unformatted text preview: 0 2.00 CHAPTER 2.26 (a) 2 ⎛ v f + vi ⎞ ⎛ 2.80 m s + v i ⎞ ∆x = v ( ∆t ) = ⎜ ⎟ ( 8.50 s ) , ⎟ ∆t becomes 40.0 m = ⎜ ⎝ ⎠ 2 ⎝2⎠ which yields v i = 6.61 m s . (b) a = 2.27 v f − vi ∆t = 2 .80 m s − 6.61 m s = − 0.448 m s 2 8.50 s Suppose the unknown acceleration is constant as a car initially moving at v i = 35.0 m i h comes to a v f = 0 stop in ∆x = 40.0 ft . We find its acceleration from v 2 = v i2 + 2 a( ∆x ) . f 0 − ( 35.0 m i h ) ⎛ 1.47 ft s ⎞ 2 a= = ⎜ 1 m i h ⎟ = − 33.1 ft s . 2 ( ∆x ) 2 ( 40.0 ft ) ⎝ ⎠ v 2 − v i2 f 2 2 Now consider a car moving at v i = 70.0 m i h and stopping to v f = 0 with a = − 33.1 ft s 2 . From the same equation its stopping distance is ∆x = 2.28 v 2 − v i2 f 2a 0 − ( 70.0 m i h ) ⎛ 1.47 ft s ⎞ = ⎜ ⎟ = 160 ft 2 −33.1 ft s 2 ⎝ 1 m i h ⎠ 2 ( 2 ) (a) From the definition of acceleration, we have a= v f − vi t = 0 − 40 m s = − 8.0 m s 2 . 5.0 s 1 (b) From ∆x = v i t + at 2 , the displacement is 2 ∆x = ( 40 m s ) ( 5.0 s ) + 2.29 ( ) 1 2 −8.0 m s 2 ( 5.0 s ) = 100 m . 2 (a) With v f = 120 km h , v 2 = v i2 + 2a( ∆x ) yields f 2 ⎡(120 km h ) 2 − 0⎤ ⎣ ⎦ ⎛ 0.278 m s ⎞ = 2.32 m s 2 . a= = ⎜ 1 km h ⎟ 2 ( ∆x ) 2 ( 240 m ) ⎝ ⎠ v 2 − v i2 f 29 CHAPTER (b) The required time is t = 2.30 v f − vi a = 2 (120 km h − 0) ⎛ 0.278 m s ⎞ = 14.4 s . 2 .32 m s 2 ⎜ 1 k m h ⎟ ⎝ ⎠ (a) The time for the truck to reach 20 m s is found from v f = v i + at as t= v f − vi a = 20 m s − 0 = 10 s . 2.0 m s 2 The total time is t total = 10 s + 20 s + 5.0 s = 35 s . (b) The distance traveled during the first 10 s is 0 + 20 m ⎝ 2 ( ∆x )1 = v1t1 = ⎛ ⎜ s⎞ ⎟ (10 s ) = 100 m . ⎠ The distance traveled during the next 20 s (with a = 0) is ( ∆x ) 2 = ( v i ) 2 t 2 + a2t 22 = ( 20 m s ) ( 20 s ) + 0 = 400 m . 1 2 The distance traveled in the last 5.0 s is ( ∆x ) 3 = v 3t 3 = ⎛ ⎜ ⎝ 20 m s +0 ⎞ ⎟ ( 5.0 s ) = 50 m . ⎠ 2 The total displacement is then ∆x = ( ∆x )1 + ( ∆x ) 2 + (...
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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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