A box of mass *m* is released from rest at position on the frictionless curved track shown above. It slides a distance *d* along the track in time *t* to reach position , dropping a vertical distance *h. *Let *v* and *a* be the instantaneous speed and instantaneous acceleration, respectively, of the box at position . Which of the following equations is valid for this situation?

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The correct answer is . This equation is an application of conservation of mechanical energy. In this situation the loss of potential energy *mgh* is equal to the gain of kinetic energy . The other four equations are all kinematics equations that apply only when the acceleration is constant. Since the track is curved, the component of the gravitational force on the box that is tangent to the surface of the track decreases as the box slides. It is this component of the gravitational force that accelerates the box. By Newton’s second law, , as the force decreases the acceleration also decreases. Since the acceleration is not constant, the other four equations are not valid.