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I was doing my homework and I came across the question:

Suppose that two objects, each with the same mass, are accelerated from rest to the same velocity. The force that accelerates one object is much larger than the force that accelerates the other object but acts for a shorter time. The work done by the larger force is:

  1. smaller than the work done by the smaller force.
  2. larger than the work done by the smaller force.
  3. equal to the work done by the smaller force.
  4. insufficient information to determine.

I answered 2, it would be larger than the work done by the smaller force. I thought this was correct because I thought that a larger force meant more work done, but this answer was wrong.

Please help me understand this, I think the answer might be that the work is equal but I'm not sure and need an explanation.

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  • $\begingroup$ One way to work things out is to run the numbers. Set the lower force as equal to 1/2 the greater force. Then calculate. How long would it take half the force to cause the object to reach the same speed. Answer, twice as long. Then calculate the distance (average speed x time) and you're 90% there. Sathyaram's way works too. :-) $\endgroup$
    – userLTK
    Nov 12 '15 at 4:00
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HINT: WORK-ENERGY PRINCIPLE
The work done by all forces acting on a particle (the work of the resultant force) equals the change in the kinetic energy of the particle.
Here the answer will be option-3 equal work done.

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