What happens if an object (plane or space ship) travels at a speed less than that of earth rotation?
The stationary plane and the atmosphere were already moving at the speed of Earth's rotation. Because of this, the Earth's rotational speed really has very little effect on aircraft speed. To answer the second part of your question, almost all passenger jets fly slower than the Earth's rotation. The Earth rotates at 1675 km/hr at the equator; average cruise speed is 878-926 km/hr.