Final answer:
Position and displacement are the quantities that depend on the choice of origin in a coordinate system, as they are vector quantities that relate to a specific point. Speed, average velocity, and instantaneous velocity are independent of the choice of origin.
Step-by-step explanation:
In a coordinate system, certain quantities depend on the choice of origin, while others do not. The quantities that depend on the choice of origin are position and displacement. These are both vector quantities, which means they have both magnitude and direction relative to a chosen origin point. On the other hand, speed, average velocity, and instantaneous velocity do not depend on the choice of origin as they only describe how fast something is moving and not where it is moving to or from.
To further clarify with an example, if a car travels from point A to point B along a straight line, the distance it travels is a scalar quantity that is always positive and does not depend on where the origin is placed. The displacement is the shortest path from A to B, which is a vector that points from A to B. Its magnitude and direction depend on the locations of A and B, thus depending on the choice of origin. The car's speedometer measures speed, which is the magnitude of how fast the car is going, and is independent of the car's position or displacement.
If the car's path from point A to B was straight, and we measure how long it took to travel, dividing the distance by the time would give us the average speed, which would be the same as the magnitude of the average velocity in this particular case since there is no change in direction. However, if the car had taken a more scenic route with turns and perhaps even retracing some of its paths, while its speed might remain relatively constant, the displacement would be different, and so the magnitude of the average velocity would likely be less than the average speed.