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In an online test the following question was asked:

The motion of a mass is described by $s=2t$ where $s$ is displacement and the force on it by $F=e^t$. What is the work done by it? Their answer was the usual integration of force with displacement by the substitution of $ds=2dt$.

But $s=2t$ describes the motion of a particle with a constant velocity which means no acceleration and so no work. So shouldn't the work done be zero?

Qmechanic
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Theoretical
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1 Answers1

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Your statement "no acceleration and so no work" applies to the total work done on the object. But the question appears to be "What is the work done by this force?" There must be some equal and opposite force acting (to prevent acceleration) but the problem doesn't ask you about that.

For instance, this might describe the work done pushing an object up a slope with steadily increasing coefficient of friction. Positive work is required to push the object up the slope, while both gravity and friction do negative work. The total work done is zero, but it is physically relevant to separately calculate the work done by the force pushing the object, the work done by friction, and the work done by gravity (the increase in potential energy).

Justin Freeman
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  • this is probably the right answer, but still the question as quoted says "The motion of a mass is described by ... the force ...", which suggests the motion is supposed to be produced by this force. The question is simply badly formulated. – Umaxo Jul 31 '20 at 11:09