Which of the following best explains how $velocity$ differs from $speed$, and why $velocity$ is considered a $vector$ quantity?

• A. $Velocity$ and $speed$ are both $vectors$ because they both require direction to be fully described.
• B. $Velocity$ and $speed$ are both $scalar$ quantities because they only measure how fast an object moves.
• C. $Velocity$ is a $scalar$ because it measures the rate of change of distance, while $speed$ is a $vector$ because it measures the rate of change of displacement.
• D. $Velocity$ includes both magnitude and direction, while $speed$ includes only magnitude; $velocity$ is a $vector$ because it describes both how fast and in what direction an object moves.

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the definitions of speed and velocity. Speed is a scalar quantity that measures how fast an object is moving, regardless of direction. Velocity, on the other hand, is a vector quantity that measures how fast an object is moving and in which direction.
2. Step 2: Recognize that scalar quantities have only magnitude (a numerical value), while vector quantities have both magnitude and direction. This distinction is crucial in physics to fully describe motion.
3. Step 3: Note that speed is the rate of change of distance with respect to time, which does not require direction. Mathematically, speed = \( \frac{\text{distance}}{\text{time}} \).
4. Step 4: Understand that velocity is the rate of change of displacement with respect to time. Displacement is a vector quantity that includes direction, so velocity must also include direction. Mathematically, velocity = \( \frac{\text{displacement}}{\text{time}} \).
5. Step 5: Conclude that velocity is considered a vector because it fully describes both how fast an object moves and the direction of its motion, whereas speed only describes how fast without any directional information.