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Velocity and acceleration are fundamental concepts in physics that describe the rate of change in position and velocity of an object.
Velocity is defined as the rate of change in time of the displacement. To know the velocity of an object one must know both how fast the displacement is changing and in what direction. Therefore, it is also well represented by a vector.
Acceleration, being the rate of change of velocity also requires both a magnitude and a direction relative to some coordinates.
Speed differs from velocity because speed is how fast something moves without regard to direction.
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