In one-dimensional motion, how are speed and velocity related?

• A. Speed is the magnitude of velocity: $s=\left|v\right|$.
• B. Velocity is the magnitude of speed: $v=\left|s\right|$.
• C. Speed is a vector quantity and velocity is a scalar quantity.
• D. Speed and velocity are always equal because they both include direction.

Answer: (A)

Verified step by step guidance

1. Understand the definitions: Velocity is a vector quantity, meaning it has both magnitude and direction, while speed is a scalar quantity, meaning it only has magnitude and no direction.
2. Recognize that in one-dimensional motion, velocity can be positive or negative depending on direction, but speed is always positive or zero since it represents the magnitude of velocity.
3. Express the relationship mathematically: speed \(s\) is the magnitude of velocity \(v\), which can be written as \(s = |v|\).
4. Note that velocity cannot be expressed as the magnitude of speed because speed has no direction; thus, velocity contains more information than speed.
5. Conclude that speed and velocity are related but not the same: speed is the absolute value (magnitude) of velocity, and velocity includes direction while speed does not.