**Unformatted text preview: **f equal 0. So, use ∆ x = v ave ∆ t, v ave = (v i + v f )/2, v f = v i + ∆ v, and ∆ v = a ∆ t. Hint: After two algebraic substitutions you get ∆ x = v i ∆ t + 1 / 2 a ∆ t 2 . Write this as 1 / 2 a ∆ t 2 +v i ∆ t - ∆ x = 0, plug in the numbers for a and v i then solve the quadratic for ∆ t. Use the quadratic formula that says if a t 2 + b t + c = 0 Then: t = (-b ± √ b 2 – 4 ac )/2 a where a = 1 / 2 a, b = v i, c = -∆ x (Don’t forget to find the final velocity) d) Now find the same final velocity using energy buckets and “work.” Show your reasoning. a = F net = box rough floor Paul...

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