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1. The problem statement, all variables and given/known data

It is more a conceptual problem. If all the variables are known, and I am asked to write x as a function of time, why the equations below are not equivalent when equation (b) is derived from (a) after substituting "v_f = v_i + at" ?

(a) x_f = x_i + 1/2(v_f + v_ i)(t)

(b) x_f = x_i + v_i(t) + 1/2(a)(t^2)

If I suppose: x_i = 0, v_f = 50, v_i = 0, t = 5, and a= 3.33. Am I supposed to get same answers? It seems not, and I don't understand why.

I could say that x = 0 + 1/2(a)(t^2) = 1/2(3.33)(t^2) or x_f = 1.67(t^2). [using (b)]

But for (a) x_f = 0 + 1/2(50)(t) or x_f = 25(t)

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# To write x as a function of time doubt.

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