A jet airplane travelling at the speed of 500 km h–1 ejects its products of combustion at the speed of 1500 km h–1 relative to the jet plane. What is the speed of the latter with respect to an observer on the ground ?
Negative sign implies that the direction of its products of combustion is opposite to the direction of motion of the jet airplane.
What is rest?
When an object does not change its position with time, with respect to it's surroundings. In such a case the object is said to be at rest.
What is the most essential thing to study the motion of a body?
The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion.