In a straight-line motion, how are speed and velocity related?

• A. Velocity is the magnitude of the speed vector, so $v=\left|\mathrm{speed}\right|$.
• B. Speed is a vector and velocity is a scalar; they differ only by units.
• C. Speed is the magnitude of the velocity vector; equivalently, $\mathrm{speed}=\left|v\right|$.
• D. Speed and velocity are always identical because both include direction.

Answer: (C)

Verified step by step guidance

1. Understand the definitions: Velocity is a vector quantity, which means it has both magnitude and direction, while speed is a scalar quantity, meaning it only has magnitude and no direction.
2. Recognize that in straight-line motion, velocity can be represented as a vector \( \vec{v} \), and speed is the magnitude (or absolute value) of this velocity vector.
3. Express the relationship mathematically: speed \( = |\vec{v}| \), where \( |\vec{v}| \) denotes the magnitude of the velocity vector.
4. Note that speed is always a non-negative value since it represents how fast an object is moving regardless of direction, whereas velocity can be positive or negative depending on the direction along the line.
5. Conclude that speed and velocity differ in that velocity includes direction and speed does not; speed is the magnitude of the velocity vector.