A net horizontal force F is applied to a box with mass M that is on a horizontal, frictionless surface. The box is initially at rest and then moves in the direction of the force. After the box has moved a distance D, the work that the constant force has done on it is WD and the speed of the box is V. The equation P = Fv tells us that the instantaneous rate at which F is doing work on the box depends on the speed of the box.
a) At the point in the motion of the box where the force has done half the total work, and so has done work WD/2 on the box that started from rest, in terms of V what is the speed of the box? Is the speed at this point less than, equal to, or greater than half the final speed?
b) When the box has reached half its final speed, so its speed is V/2, how much work has been done on the box? Express your answer in terms of WD. Is the amount of work done to produce this speed less than, equal to, or greater than half the work WD done for the full displacement D?
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