Answer
$K=4000\:\mathrm{joules}.$
Work Step by Step
We can write the given statement as a relation:
$K\:\propto\:v^2$
Let's introdue a proportionality constant $\:a\:$ to turn the relation into an equation as:
$K=a\cdot v^2$
We can find the value of $\:a\:$ when we are given $\:K=12,960\:$ and $\:v=18.$
$12960=a\cdot 18^2$
$\Rightarrow\: a=\frac{12960}{18^2}=\frac{12960}{324}$
$\Rightarrow\: a=40$
So, now our general equation $\:K=a\cdot v^2\:$ becomes:
$K=40v^2$
When $\:v=10,\:$ we have:
$K=40(10)^2$
$\Rightarrow\: K=4000$
