In the context of vectors and scalars, how are speed and velocity similar?

• A. Both are vector quantities that include direction.
• B. Both can be negative depending on the chosen coordinate system.
• C. Both describe the rate at which an object’s position changes with time.
• D. Both are always equal to the displacement divided by time.

Answer: (C)

Verified step by step guidance

1. Understand the definitions: Speed is a scalar quantity that measures how fast an object is moving, regardless of direction, while velocity is a vector quantity that includes both speed and direction.
2. Recognize that both speed and velocity describe how an object's position changes over time, which means they both relate to the rate of change of position.
3. Note that speed is the magnitude of velocity, so while velocity can be positive or negative depending on direction, speed is always non-negative.
4. Recall the formula for average velocity: \(\\vec{v} = \\frac{\\Delta \\vec{x}}{\\Delta t}\), where \(\\Delta \\vec{x}\) is displacement and \(\\Delta t\) is time; speed is the magnitude of this velocity vector.
5. Conclude that the similarity between speed and velocity is that both describe the rate at which an object's position changes with time, even though one is scalar and the other is vector.