Why kinetic energy is proportional to velocity squared

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Kinetic energy is proportional to the square of velocity due to the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy. When a constant force is applied, the rate of energy transfer increases as velocity increases, leading to greater kinetic energy at higher speeds. This means that while energy input may be constant, the resulting kinetic energy grows at an increasing rate, as seen in the example of accelerating from 5 to 10 m/s requiring more energy than from 0 to 5 m/s. The confusion often arises from the distinction between force, energy, and how they relate to changes in velocity. Ultimately, conservation of energy principles clarify that energy input translates into kinetic energy in a non-linear fashion.
  • #91
Even battery energy is rated in watt hours (or in amp hours and you have to multiply by the voltage). In this case energy = power x time.
 

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