The kinetic energy of an object depends on what?

It depends on "Potential Energy", the amount energy it could have, the amount depending on certain circumstances, like height or force. This was how traditional and some modern rollercoasters work. As the "conveyer belt" pulls you up, the higher you go, the more potential energy you have. Once you are falling down the hill, you are experiencing "Kinetic Energy". Hope it makes sence.

Since K. E = (1/2) mv²

It depends on the mass of the object and the velocity of the object as well.

KE = f (m, v)