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42_Physics ProblemsTechnical Physics

42_Physics ProblemsTechnical Physics - Chapter 2 P2.54(a...

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Chapter 2 43 P2.54 (a) See the graphs at the right. Choose x = 0 at t = 0. At t = 3 s, x = ( )= 1 2 8 3 12 m s s m a f . At t = 5 s, x = + ( )= 12 8 2 28 m m s s m a f . At t = 7 s, x = + ( )= 28 1 2 8 2 36 m m s s m a f . (b) For 0 3 < < t s, a = = 8 3 2 67 m s s m s 2 . . For 3 5 < < t s, a = 0 . (c) For 5 9 s s < < t , a = = 16 4 4 m s s m s 2 . (d) At t = 6 s, x = + ( )= 28 6 1 34 m m s s m a f . (e) At t = 9 s, x = + ( )= 36 1 2 8 2 28 m m s s m a f . FIG. P2.54 P2.55 (a) a dv dt d dt t t = = × + × 5 00 10 3 00 10 7 2 5 . . a t = × + × 10 0 10 3 00 10 7 5 . . m s m s 3 2 c h Take x i = 0 at t = 0. Then v dx dt = x vdt t t dt x t t x t t t t = = × + × = − × + × = − × + × z z 0 5 00 10 3 00 10 5 00 10 3 3 00 10 2 1 67 10 1 50 10 0 7 2 5 0 7 3 5 2 7 3 5 2 . . . . . . . e j e j e j m s m s 3 2 (b) The bullet escapes when a = 0 , at × + × = 10 0 10 3 00 10 0 7 5 . . m s m s 3 2 c h t t = × × = ×
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