The kinetic energy of an object is derived using which of the following equations of
motion?
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A.
v = u + at
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B.
a = (v – u) / t
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C.
s = ut + ½ at2
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D.
v2 – u2 = 2as
Correct Answer:
D. v2 – u2 = 2as
Explanation:
The derivation of kinetic energy is based on the work-energy theorem, where work done is equal to the change in kinetic energy. Starting with the work formula (W = Fs) and substituting Newton's second law (F = ma), we get W = mas. Using the third equation of motion, v2 - u2 = 2as, we can solve for displacement (s), which gives s = (v2 - u2) / 2a. Substituting this back into the work equation results in W = ma * [(v2 - u2) / 2a], which simplifies to W = ½mv2 - ½mu2. This shows that the work done results in a change in kinetic energy, identifying v2 – u2 = 2as as the essential equation for this derivation.
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