 For the second equation, we start with the area under the VT graph is the change in position delta S. The error is all the thing here in blue. Now we know that the area in blue is V average times delta T. How do we get there? Take off this little triangle up here and you put it right there. And you see that what before was an irregular shape is not just a rectangle with one side delta T and the other side V average. Now how do we calculate V average? V average is simply you add up the initial and the final velocity and you divide it by two. Therefore what you get is change in position is one half times V final plus V initial times delta T.