Final answer:
Deriving a force curve involves calculating the area under the force versus displacement graph to determine work done, while deriving a velocity curve involves analyzing the velocity versus time graph to determine acceleration and displacement.
Step-by-step explanation:
The difference between deriving a force curve and a velocity curve given a force and displacement curve lies in how the data is analyzed and interpreted.
To derive a force curve, one would examine the graph of force versus displacement and calculate the area under the curve. This area represents the work done on an object. The force curve can also be used to determine the change in kinetic energy using the work-energy theorem.
To derive a velocity curve, one would analyze the graph of velocity versus time. The slope of the velocity curve at any point represents the object's acceleration at that moment. The area under the velocity curve represents the displacement of the object over time.