A force increases the speed of a 1.0 kg object from 4 m/s to 8 m/s. The work done by the force will be ______.
- A.8 J
- B.32 J
- C.24 J
- D.16 J
Correct answer
Explanation
The correct answer is C, 24 J. By the work-energy theorem the work done equals the change in kinetic energy, which is half of 1.0 into 8 squared minus 4 squared, that is 0.5 × (64 - 16) = 24 joule.
Kinetic energy is given by half m v squared, so at 4 m/s the object has 8 joule and at 8 m/s it has 32 joule; the force must supply the difference of 24 joule. Note that doubling the speed makes the kinetic energy four times, because the speed is squared. The work-energy theorem holds whatever the path taken, which is why the question can be solved without knowing the force or the distance.
Option A is wrong because 8 joule is only the starting kinetic energy. Option B is wrong because 32 joule is the final kinetic energy, not the change. Option D is wrong because 16 joule comes from taking half of the difference of the squares of the speeds incorrectly.
Exam tip: work done = final kinetic energy minus initial kinetic energy, and doubling speed makes kinetic energy four times.
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