The quantity which describes the rate and the direction of motion is:

Velocity is defined as a vector quantity that includes both the rate and direction of an object's motion. In physics, velocity is expressed as the change in position (displacement) over the change in time. This distinguishes it from speed, which is a scalar quantity representing only the magnitude of motion without any directional component.

Understanding that velocity incorporates direction is crucial, especially in contexts like navigation or in analyzing movement along curved paths, where simply knowing how fast an object is traveling (speed) is insufficient.

Acceleration, while also a vector quantity, relates to the rate of change of velocity, and displacement measures the overall change in position without considering the speed or the time taken. Thus, among the given choices, velocity is the one that most accurately represents the combination of both speed and direction in the context of motion.