So I am teaching myself physics in "Physics 1 For Dummies" and I have come across a chapter dealing with deriving equations, this one being the distance through using the average velocity. I have never derived equations before, so be easy on me! So basically it starts off with s=vt (distance equals velocity times time). We take the initial and final velocity and get the average, which is v=1/2at. When this is applied to the final equation, we get s=vt=(1/2at)t Where did this extra t come from? I thought the equation for velocity was change in distance divided by change in time? Also, why do we add on another equal sign for it? I've never taken calculus so I may need to take that first, but I was hoping someone could explain.