Which equation relates distance travelled, initial velocity, final velocity, and acceleration?

The equation that correctly relates distance traveled (d), initial velocity (u), final velocity (v), and acceleration (a) is derived from the principles of uniformly accelerated motion. The appropriate equation for this relationship is:

d = (v² - u²) / (2a).

This formula is particularly useful for determining the distance traveled when you know the initial and final velocities and the acceleration. It comes from the kinematic equations of motion, which describe how an object's velocity changes under constant acceleration.

In this equation, v represents the final velocity, u represents the initial velocity, and a is the constant acceleration. The formula essentially connects these variables by rearranging the standard kinematic relationships and solving for distance.

The other choices represent different physical concepts or equations. The first option pertains to calculating displacement when considering time elapsed, initial velocity, and acceleration. The third one defines how velocity changes over time under acceleration, and the last one, f = ma, represents Newton's second law of motion, relating force, mass, and acceleration. Each of these equations has its own specific context and application within physics, but only the second option directly specifies the relationship among distance, initial and final velocities, and acceleration.