The kinetic energy of a given body depends on the :

momentum

Reason — As,

Kinetic Energy = $\frac{1}{2}$ mv²

And,

Momentum (p) = mv

Then,

$$\begin{aligned}\text {Kinetic Energy} = \frac{1}{2\text m}\text m^2 \text v^2 \\[1em] = \frac{1}{2\text m}\text p^2\end{aligned}$$

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