The kinetic energy of a given body depends on the :

momentum

Reason — As,

$\text {Kinetic Energy} = \frac{1}{2}\text m \text v^2$

And,

Momentum (p) = mv

Then,

$\text {Kinetic Energy} = \frac{1}{2\text m}\text m^2 \text v^2 = \frac{p^2}{2\text m}$

So, the kinetic energy of a given body depends on its momentum.