The kinetic energy of an object is derived using which of the following equations of motion?
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A.
s = ut + ½ at2
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B.
v = u + at
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C.
a = (v – u) / t
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D.
v2 – u2 = 2as
Correct Answer:
D. v2 – u2 = 2as
Explanation:
The kinetic energy formula is derived using the third equation of motion, v2 – u2 = 2as. By starting with the definition of work done (W = Fs) and substituting force with mass times acceleration (F = ma), the expression becomes W = mas. From the motion equation, displacement (s) can be expressed as (v2 – u2) / 2a. Substituting this value into the work equation results in W = ma * (v2 – u2) / 2a, which simplifies to ½mv2 – ½mu2. This represents the change in kinetic energy, establishing the relationship between work and the energy of motion.
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