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Work: the transfer of energy 

Positive work: The attempt to speed an object up 

Force: A push or a pull on an object

Displacement:vector that describes the difference between final and initial position

Positive Work 

 When talking about negative and positive work it is important to consider what work is and why we calculate work.  There are two ways of looking like work.

The first way is work is done when one form of energy is transformed into another, now we haven't talked about energy but understand that there is two types of mechanical stored and motion based.  To transform motion energy to stored energy work has to be done, or vise verse, even transforming one form of stored energy to another work has to be done.  

The second way of looking at work is to change the speed (not the velocity) of an object.  This idea of work where positive and negative makes the most sense.  Positive work is an attempt to speed and object up, negative work is an attempt to slow an object down.  It is very important to understand that it is not velocity we are talking here but only speed.   So positive work does not create a larger positive velocity, and negative work does not create a smaller positive velocity.

Example

You have signed up for a experiment in perception.  You are shown a series of pictures.  The first picture is of a rocket sled on a friction-less track, the rockets on the back have been fired.  The caption under the pictures says " at time equal zero the rockets are fired pushing the sled to the right (the positive x direction)".  The second picture shows the rocket sled 100 meters down the track the rockets are still on.  The caption under the picture says "after 2 secs the sled has traveled 100 m to the right (in the positive x direction)".  

The Question is asked:  "Based on the pictures do you expect the sled to be moving slower or faster?"    What do you think? 

 Most of us would believe that the sled would be going faster, and as long as there is no tomfoolery, like additional forces acting ton the sled, you would be right.

Example 2:

Consider this, if you were shown two similar pictures but instead the rocket sled is pushed to left and after 2 seconds the sled has moved 100m to the left and you are asked the same question how would you respond? 

Most of us would say that the sled would be moving faster, an once again if no trickery, you would be right.  

 Both the of these situations are examples of positive work, when considering weather its positive work both the force and displacement vectors must be pointing in the same direction.  

To stress the point even more if you drop and object off the cliff, force of gravity is down and the displacement is down (after a second or two its moved down a few meters), and the object has sped up.