He was also the first to use the word energy with its current meaning in a lecture on collisions given before the Royal Institution. Thomas Young (1773–1829) derived a similar formula in 1807, although he neglected to add the ½ to the front and he didn't use the words mass and weight with the same precision we do nowadays. Thus an object's kinetic energy is defined mathematically by the following equation… Naturally, the kinetic energy of an object at rest should be zero. The integral of which is quite simple to evaluate over the limits initial speed ( v) to final speed ( v 0). Rearrange the differential terms to get the integral and the function into Again, start from the work-energy theorem and add in Newton's second law of motion (the calculus version). Therefore, we don't need the second term and an object's kinetic energy is just…ĭerivation using calculus (but now we don't need to assume anything about the acceleration). If kinetic energy is the energy of motion then, naturally, the kinetic energy of an object at rest should be zero. v 2 = v 0 2 + 2 a∆ sĪnd now something a bit unusual. Take the the appropriate equation from kinematics and rearrange it a bit. Start from the work-energy theorem, then add in Newton's second law of motion. Let's do it twice.ĭerivation using algebra alone (and assuming acceleration is constant). Kinetic energy is a simple concept with a simple equation that is simple to derive.
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