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(a)

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Weight of book box Fg = 209 N

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Gravitational acceleration g = 9.8 m/s

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Fg = mg

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m = 209/g

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m = 209/9.8

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m = 21.33 kg

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Shoved force Fs = 430 N

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Shoved angle with horizontal = 35º

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Friction coefficient µ = 0.57

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Book box moved distance s = 5 m

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Horizontal Shoved force Fsh = Fs(cos35) = 430*0.819

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Fsh = 352.24 N

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Vertical Shoved force Fsv = Fs(sin35) = 430*0.5736

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Fsv = 246.65 N

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Vertical component of forces Fn = Fsv + Fg

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Fn = Net force in vertical direction

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Fn = 246.65 + 209

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Fn = 455.65 N

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Force due to friction Ff = µFn

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Ff = 0.57*455.65

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Ff = 259.72 N

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Resultant force(F) is remained shoved force when frictional loss forces subtracted in horizontal direction.

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F = Fsh-Ff

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a =  acceleration of Book box.

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ma = 352.24 - 259.72

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21.33a = 92.52

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a = 4.337

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From motion equations

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s = ut + ½at²

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Box starts from rest.So initial velocity u = 0

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5 = 0 + ½(4.337)t²

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t² = 5*2/4.337

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t = 1.52 sec

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Solution is 1.52 sec

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