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Definition of Work:
When a force acts upon an object to cause (or to hinder) a displacement, work is done upon the object. Mathematically, work is the dot product of the force and displacement for such a situation.
Definition of Power:
Power is the rate at which work is done upon an object.
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Work is the task-related quantity that depends on the amount of force exerted and the amount of displacement it causes. If students A and B are doing identical tasks, then they are doing the same work. But power is the task- and time-related quantity that has to do with the rate at which the work is done. The student who does the task in the least amount of time is working faster - that is, doing the work at a greater rate. Thus, the student who completes the same task in the least amount of time has the greater power rating.
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