A child applies a force F parallel to the x-axis to a 10.0-kg sled moving on the

Question

A child applies a force F parallel to the x-axis to a 10.0-kg sled moving on the frozen surface of a small pond. As the child controls the speed of the sled, the x -component of the force she applies varies with the x -coordinate of the sled as shown in the figure. Suppose the sled is initially at rest at x = 0. You can ignore friction between the sled and the surface of the pond. Use the work-energy theorem to find the speed of the sled at 8.0 m. Use the work-energy theorem to find the speed of the sled at 12.0 m.

Explanation / Answer

work done=integral of Fdx now work done in moving from 0 to 8= area under the curve=1/2*8*10=40J this energy is converted to velocity of the sled hence mv*v/2=40 m=10kg so v=2sqrt2 m/s to find the velocity at x=12 we need net work done work done=60J so m*v*v/2=60 hence v=2sqrt6 m/s

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