Question

A student wearing frictionless roller skates on a horizontal surface is pushed by a friend with a constant force of 55 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 362 J? Show your work.

Answer 1

Using the work-energy principle, the student on frictionless roller skates must be pushed 6.58 meters by a constant force of 55 N to achieve a final kinetic energy of 362 J.

Step-by-step explanation:

To solve how far the student must be pushed so that her final kinetic energy is 362 J, we utilize the work-energy principle, which states that the work done on the student equals the student's change in kinetic energy (Work = ΔKE).

Since the student starts from rest, the initial kinetic energy (KEi) is 0 J, and the final kinetic energy (KEf) is given as 362 J. Therefore, the work done on the student by the force is also 362 J. Work is calculated by the formula: Work = Force x Distance.

Substituting the given values:

1. Work = 55 N x Distance
2. 362 J = 55 N x Distance
3. Distance = 362 J / 55 N = 6.58 m

Therefore, the student must be pushed a distance of approximately 6.58 meters.