To write x as a function of time doubt.

[naaa00]

Hello!

Homework Statement

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)

 

[Doc Al]

If I suppose: x_i = 0, v_f = 50, v_i = 0, t = 5, and a= 3.33.

These numbers don't make sense. (You can't just pick arbitrary values and expect it to work.)

 

[naaa00]

Ok. But may I ask two more questions?

(a) Why these numbers do not make sense? physicaly impossible? What sort of numbers would make sense?

(b) And if looked from a mathematical point of view, why both equations must have particular values in order to be equivalent? Or are they not equivalent?

 

[Doc Al]

Ok. But may I ask two more questions?

(a) Why these numbers do not make sense? physicaly impossible? What sort of numbers would make sense?

Yes, those numbers are physically impossible. For example: If vi = 0, vf = 50, t = 5, then a is determined by the physics to be 50/5 = 10 m/s².

(b) And if looked from a mathematical view, why both equations must have particular values in order to be equivalent? Or are they not equivalent?

They are equivalent.

 

[naaa00]

...

Well, now I see clearly the mistake. I am only going to say that this is depressing. Perhaps I need some rest.

Thank you!