I am a creature of habit.

Once I have something memorized and have used it enough times to be comfortable with it, I tend to stick with it and not try to learn new ways of looking at things, because doing so tends to confuse me.

I have gone through almost an entire set of problems using the same set of two or three equations, getting all of them right, and then I get to the last 5 and they’re all wrong. I look at the solutions, and all of the ones I got wrong use an equation I’ve never seen before. But the problems seem just like the other 25 I’ve done with my other equations!!! ARGH!!! *ripping hair*

To shed some light on the situation:

The equations I’ve been using are these:

x (final) = x (initial) + [velocity (inital) * time] + [1/2(acceleration) * time^2]

and

velocity (final) = velocity (initial) + [acceleration * time].

The new equation that I’ve never seen before is this:

[velocity (final)]^2 = [velocity (initial)]^2 + [2 *acceleration * x (final)].

Where did this come from? Why would it work in a situation where the previous two equations wouldn’t? For that matter, in what situations would the previous two NOT work, and why?

Just so you know–this is not about getting this problem set done; it was due and was finished a long time ago; I am just genuinely perplexed by this and cannot go to sleep ignorant.

I’d appreciate any attempt at explaining this–if you would like the specific problems, just ask.