In introductory mechanics, what do speed and velocity have in common?

• A. Both are vector quantities that include direction.
• B. Both are always equal to the displacement divided by time.
• C. Both describe how fast an object’s position changes with time (the rate of motion).
• D. Both can be negative in one-dimensional motion.

Answer: (C)

Verified step by step guidance

1. Understand the definitions of speed and velocity: Speed is a scalar quantity that measures how fast an object is moving, while velocity is a vector quantity that measures both the speed and the direction of the object's motion.
2. Recognize that both speed and velocity describe the rate at which an object's position changes with time, meaning they both relate to how quickly an object moves.
3. Note that speed is always non-negative because it does not include direction, whereas velocity can be positive or negative depending on the direction of motion in one-dimensional cases.
4. Recall that velocity is defined as displacement divided by time, which includes direction, while speed is defined as the total distance traveled divided by time, which does not consider direction.
5. Conclude that the commonality between speed and velocity is that both describe how fast an object's position changes with time, i.e., the rate of motion, but they differ in whether direction is included.