I'm trying to understand the "Why" of this equation but can't make sense of it, my intuition breaks down.
When I think intuitively of energy, I think of "How powerful the impact will be if an object collides with me". Let's say a 5kg object flying at 100kmh at me. I think of this as having a lot of energy, while 100 grams flying at 1kmh having little energy. I also think about how can I make use of it, maybe dropping the weight and compressing a spring to transfer it to something else, seems like mass and velocity is all I need.
Now, if I had to guess the formula of energy I would say that all that matters is the final velocity and the mass. I would imagine energy being m * v. But it's not.
Studying energy I keep encountering counter intuitive explantations and data that I feel like I don't need.
One being distance. Why would I care about the distance? If an 5kg object collides with me at 100kmh I don't even know where it comes from (or the distance it traveled) or how it accelerated... nor do I care, if I want to compress a spring with that energy it's irrelevant how it accelerated or the distance traveled. Why it makes a difference if the object was accelerated by gravity or teleported at 5 meters of my spring if both will have the same result on collision.
I get that If I have a 2kg object at 20m height and I drop it, to calculate the energy I have to make use of acceleration due to gravity. But for my brain, this is just to calculate the final velocity before impact, but it's not, as I need to divide mass by half as I take the average velocity, which seems to me is data that I don't need.
If someone can help me map this into my head and build intuitive thinking, don't want to end up just memorising and copy pasting the formula.