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41_Physics ProblemsTechnical Physics

# 41_Physics ProblemsTechnical Physics - 42 Motion in One...

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42 Motion in One Dimension Section 2.7 Kinematic Equations Derived from Calculus P2.53 (a) J da dt = = constant da Jdt = a J dt Jt c = = + z 1 but a a i = when t = 0 so c a i 1 = . Therefore, a Jt a i = + a dv dt dv adt v adt Jt a dt Jt a t c i i = = = = + = + + z z b g 1 2 2 2 but v v i = when t = 0, so c v i 2 = and v Jt a t v i i = + + 1 2 2 v dx dt dx vdt x vdt Jt a t v dt x Jt a t v t c x x i i i i i = = = = + + F H G I K J = + + + = z z 1 2 1 6 1 2 2 3 2 3 when t = 0, so c x i 3 = . Therefore, x Jt a t v t x i i i = + + + 1 6 1 2 3 2 . (b) a Jt a J t a Ja t i i i 2 2 2 2 2 2 = + = + + a f a a J t Ja t
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