A block of mass m is placed on a horizontal surface. A const...

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A block of mass m is placed on a horizontal surface. A constant horizontal force F is applied to the block, causing it to move to the right from rest, covering a distance x. After the block has moved this distance, the force F is suddenly removed. The coefficient of kinetic friction between the block and the surface is . What is the speed of the block when the force F is removed?

1. Work Done by the Applied Force:

When the force is applied to the block, it accelerates and moves a distance . The work done by the applied force is:

2. Work Done by the Frictional Force:

The frictional force is given by:

The work done by the frictional force is negative (since friction opposes the motion):

3. Net Work Done on the Block:

The net work done on the block is the sum of the work done by the applied force and the work done by friction:

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