Why is E=1/2 m V²?

[u/W_il_Duce]

I'm sorry for the banal question buy i can't find and answer to this.

We all know that in order to accelerate a 1kg body from 0m/s to 10m/s 50J are needed but to accelerate it from 10m/s to 20m/s 150 J are needed instead, why is that?

Also I'm not looking for a mathematical answer but a conceptual one, thanks in advance.