A student wearing frictionless in-line skates on a horizontal surface is pushed, from rest, by a friend with a constant force of 45 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 352 J?
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To determine the distance the student must be pushed, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done on the student is equal to the force applied multiplied by the distance over which the force is applied:
Work = Force × Distance
We are given the force applied by the friend, which is 45 N. However, we don't know the distance yet.
The work done on the student is also equal to the change in kinetic energy. We are given that the final kinetic energy is 352 J, and the student starts from rest, so the initial kinetic energy is 0 J. Therefore, the change in kinetic energy is:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Change in Kinetic Energy = 352 J - 0 J
Change in Kinetic Energy = 352 J
Since the work done is equal to the change in kinetic energy, we can equate the two equations:
Work = Change in Kinetic Energy
45 N × Distance = 352 J
To find the distance, we need to rearrange the equation:
Distance = Change in Kinetic Energy / Force
Plugging in the given values:
Distance = 352 J / 45 N
Calculating the distance:
Distance = 7.82 meters
Therefore, the student must be pushed a distance of approximately 7.82 meters to achieve a final kinetic energy of 352 J.