The kinetic energy of an object is derived using which of the following equations of motion?
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A.
a = (v – u) / t
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B.
s = ut + ½ at2
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C.
v = u + at
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D.
v2 – u2 = 2as
Correct Answer:
D. v2 – u2 = 2as
Explanation:
The correct answer is v2 – u2 = 2as.
The work-energy theorem states that the work performed on an object equals its change in kinetic energy. When a constant force (F = ma) acts on an object of mass (m) over a distance (s), the work done is W = mas. Using the third equation of motion, v2 – u2 = 2as, we can express acceleration and displacement as as = (v2 – u2) / 2. Substituting this into the work equation gives W = ½m(v2 – u2). If the object starts from rest (u = 0), the work done, and thus the kinetic energy (KE), is represented by the formula KE = ½mv2, which is derived directly from the relationship established in the equation v2 – u2 = 2as.
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