# Am I wrong or the teacher?

-Physician
Okay, so our teacher gave us to define s=vt. Now i did it like that:
s=vt=(v_0+at)t=v_0 t+at2, but then, teacher said that's wrong, it should give you s=v_0 t+ \frac{1}{2} at2 Who is wrong me or teacher, If I am wrong, tell me where is my mistake, if the teacher is wrong let me know, thanks!

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tskuzzy
I am assuming that this is a problem concerning the motion of a particle under uniform acceleration. In that case, the teacher is correct. The equation ## s = vt ## is only correct for constant velocity. If velocity is not constant, then you must replace ## v ## with the average velocity.

Under uniform acceleration, the average velocity is simply ##\frac{v_0+v_f}{2}##.

Mentor
Okay, so our teacher gave us to define s=vt. Now i did it like that:
s=vt=(v0+at)t=v0t+at^2, but then, teacher said that's wrong, it should give you s=v0t+1/2at^2. Who is wrong me or teacher, If I am wrong, tell me where is my mistake, if the teacher is wrong let me know, thanks!

You are wrong.

Are you familiar with calculus? Derivatives and integrals? That's one way to derive those equations.

-Physician
I am assuming that this is a problem concerning the motion of a particle under uniform acceleration. In that case, the teacher is correct. The equation ## s = vt ## is only correct for constant velocity. If velocity is not constant, then you must replace ## v ## with the average velocity.

Under uniform acceleration, the average velocity is simply ##\frac{v_0+v_f}{2}##.
So that would be ##s=vt=\frac{v_0+v_f}{2}t=v_0 t + \frac{1}{2}##at2 or ##s=vt=\frac{v_0+v_f}{2}t=v_f t - \frac{1}{2}##at2

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tskuzzy
So that would be ##s=vt=\frac{v_0+v_f}{2}t=v_0 t + \frac{1}{2}## at2 or ##s=vt=\frac{v_0+v_f}{2}t=v_f t - \frac{1}{2}## at2

Right?
Yes that is correct.