The kinetic energy of a given body depends on the:

momentum

Reason — As kinetic energy = $\frac{1}{2}$ mv ²

If we multiply and divide by m then we get, $\frac{\text{(mv)}^2}{2\text{m}}$

As mv = momentum (p), so

kinetic energy = $\frac{\text{p}^2}{2\text{m}}$

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