In high school physics, I was taught three different equations related to accelerated motion:
- $v=at$
- $x=\frac{1}{2}at^2$
- $x=vt$
As one does in high school physics, I pretty much just mindlessly used these equations to get an okay-ish passing grade and didn't think about them much. However, I recently noticed that, when using equations 2 and 3 to form $vt=\frac{1}{2}at^2$ and solving for $t$, I got $v=\frac{1}{2}at$. Predictably, using this equation to calculate velocity yields incorrect results. I know acceleration is defined as velocity per time (without any $\frac{1}{2}$ in there), so I think I understand why this equation doesn't work, but I don't understand how deriving from two (as far as I know) correct equations can yield an incorrect one. What's up here (layman's terms would be appreciated)?