In one-dimensional motion, which statement correctly distinguishes speed from velocity?

• A. Speed is a scalar that depends only on the magnitude of motion, while velocity is a vector that includes both magnitude and direction.
• B. Speed and velocity are both vectors because they always require a direction.
• C. Velocity is a scalar equal to the total distance traveled divided by time, while speed is displacement divided by time.
• D. Speed can be negative when moving in the negative direction, while velocity is always nonnegative.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the definitions of speed and velocity in one-dimensional motion. Speed is a scalar quantity, meaning it only has magnitude (size) and no direction. Velocity is a vector quantity, meaning it has both magnitude and direction.
2. Step 2: Recognize that speed is calculated as the total distance traveled divided by the time taken, which does not consider direction. Mathematically, speed = \frac{\text{distance}}{\text{time}}.
3. Step 3: Understand that velocity is calculated as displacement divided by time, where displacement is a vector quantity representing the change in position with direction. Mathematically, velocity = \frac{\text{displacement}}{\text{time}}.
4. Step 4: Note that because velocity includes direction, it can be positive or negative depending on the direction of motion, while speed is always nonnegative since it only measures magnitude.
5. Step 5: Conclude that the correct distinction is: speed is a scalar depending only on magnitude, while velocity is a vector including both magnitude and direction.