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In all the places I've looked kinetic energy is derived from the definition of work, but I don't understand how the definition of work was developed with out the concept of kinetic energy. My question really is:
What is the logic behind the definition of work without referring to kinetic energy?
OR
What is the logic behind the definition of kinetic energy without referring to work?
Imagine for a moment that you don't know anything about work or energy, you only know Newtons second law that introduces the notion of a force and that it is related to acceleration. You also know that there are different kind of forces like gravity or the electric force. Then, by some ingenious strike of yours you say lets multiply force by distance and lets call the resulting quantity energy (or work). You then set forth to explore how this quantity behaves in various situations, for example you could compute the energy of an accelerated particle. Because this will happen really often you call the result kinetic energy. Then imagine a body, subject to gravitation and you compute the energy again and call the result potential energy. You get the idea. In our derivation we set up force as the first principle and build the notion of energy on top of it.
It now so happens that you could go the other way round, i.e. you can set up the concept of energy as your first principle and define kinetic energy by 0.5mv^2 and the potential of a gravitating body and from this derive the concept of a force by energy/distance. Most modern theories go this way but both approaches are valid.
I hope that helps.
Edit: The important thing with both approaches is that we observe the thing that we call energy to be conserved in nature (It is a very strong observation since so far we've never found any experiment to violate it. We call it the 1. law of thermodynamics). We could e.g. define energy = force times distance ^2. We would get another result for kinetic energy and potential energy of course. But then we won't find that energy is conserved
The most basic definition of energy goes as: Energy( kinetic or potential) is the capacity to do work.Consequently, energy and work are complimentary to each other. A ball thrown up gains (potential) energy, and obeying the above definition, it ends up falling back onto the earth( i.e.,it does WORK - facilitated by the gravitational force). An object moving with some velocity(i.e.,it has kinetic energy, which it acquired due to some kind of FORCE) along the direction of the causal force is clearly doing WORK(force * displacement). In both the above cases,FORCE is the primary cause and displacement suffered by the object is it's visible manifestation.Hence, it is essential to include both F & d in the formula for work. So, computing the values of kinetic energy and work really gives us an idea of how "powerful" or "capable" the the culprit(or FORCE) was ,or how "vulnerable" the victim (the object in question) was that it had to change its initial state of MOTION or REST. Thus, it really doesn't matter whether we start at kinetic energy to derive work or go the other way round, both approaches are equally justifiable.
