First answer to the question (work = force * distance):
This first answer serves to give you the main idea:
First answer modified to consider directions of force and motion (work = force * displacement in direction of force):
The previous answer applies only if the net force is in same the direction as the motion. More correctly:
The key difference here is the use of the word 'displacement' rather than 'distance'. Since a displacement, unlike a distance, can be positive or negative, so the work done by a force can be positive or negative.
Another thing to keep in mind for the future is that the displacement is to be in the direction of the force. A negative displacement therefore denotes a displacement in the direction opposite the force. We will later encounter instances where the force is not directed along the line on which the object moves, in which case the work will be defined as the force multiplied by the component of the displacement in the direction of the force.
Sometimes we will want to think in terms of the forces exerted ON objects, sometimes in terms of the forces exerted BY objects. The above statement of the work-KE theorem is in terms of the forces exerted ON an object.
The basic idea is simple enough.
The above ideas are expanded below to consider forces exerted ON objects vs. forces exerted BY objects.
Synopsis of work-kinetic energy:
First be aware that because of Newton's Second Law, there are typically two equal and opposite net forces, the net force which acts on a system and the net force which is exerted by the system. It is necessary to be careful when we label our forces; it's easy to mix up forces exerted by a system with forces exerted on the system.
The first basic principle is that the work by the net force acting ON the system is equal and opposite to the work done by the net force exerted BY the system.
The KE, on the other hand, is purely a property OF the system.
The kinetic energy change OF the system is equal to the work done by the net force acting ON the system.
The kinetic energy change OF the system is therefore equal and opposite to the work done by the net force exerted BY the system.
Intuitively, when work is done ON a system things speed up but when the system does work things have to slow down. A more specific statement would be
If positive work is done ON a system, the total kinetic energy of the system increases.
If positive work is done BY a system, the total kinetic energy of the system decreases.
(We could also state that if negative work is done ON a system, its total KE decreases, which should be easy to understand. It is also the case that if a system does negative work, its total KE increases; it's easy to see that this is a logical statement but most people fine that somehow it seems a little harder to grasp).
Below we use `dW_net_ON for the work done by the net force acting ON the system, and `dW_net_BY for the work done by the net force being exerted BY the system.
The work-kinetic energy theorem therefore has two basic forms:
The first form is
`dW_net_ON = `dKE
which states that the work done by the net force acting ON the system is equal to the change in the KE of the system.
The second form is
`dW_net_BY + `dKE = 0
which implies that when one of these quantities is positive the other is negative; thus this form tells us that when the system does positive net work its KE decreases.
Summary:
One alternative way of stating the work-kinetic energy theorem:
Forces exerted on the system are equal and opposite to forces exerted by the system, so