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Why do two formulas $d = v_0 t + \frac{at^2}{2}$ and $d=vt$ yield different results?

All of you are sure to be familiar with these two equation:

$d = v_0 t + \frac{at^2}{2}$ and $d=\overline vt$

Given the same initial and final velocities, and time and acceleration. With the second equation I need not use the acceleration. But the distance found using these equations are different!

For this who say that the second equation assume a = 0, it isn't always true. I use the formula for graphs of uniformly accelerated motion to find the distance travelled at the end of certain time. I use initial and final velocities to find the average velocity and multiply the velocity by the time in second on the graph.

Wait, I just tested another uniformly accelerated motion problem with both formulas. The result are the same! What? This is only for some specific problems.

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