Question

What kind of energy do objects have? Why can objects only have this one kind of energy?

Answer 1

An object have kinetic energy because the kinetic energy of an object is the energy it has because of its motion.

Answer 2

If the object is not moving then it has potential energy (also sometimes called stored energy) which is waiting to be used. If the object is moving then the potential energy is converted into kinetic energy (aka moving energy) because of motion.  

Objects have one kind of energy because the energy inside them is always changing from one type of energy to another.