What is the formula for the velocity of a mass after moving a distance d?

The formula for the velocity of a mass after moving a distance can indeed be connected to the work-energy principle, making the chosen answer appropriate. According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. When a force is applied to an object, it does work on that object, resulting in a change in its velocity.

To delve deeper, the work done by a constant force (which is equal to force times distance) translates into kinetic energy. If we know the initial velocity and apply force over a distance, we can derive the final velocity using the relationship between work and energy. The formula relating work done (W = F * d), where 'F' is force and 'd' is distance, allows us to connect force to velocity through kinetic energy equations.

This connection shows how acceleration (derived from force over mass) affects the velocity gained as the object moves a distance 'd'. Hence, using the work-energy principle to derive the velocity is not only valid but a comprehensive approach that integrates concepts of energy, force, and motion, confirming the correctness of the selected answer.

The other responses do not accurately capture this relationship. The first option, while a simple definition of velocity, lacks