Which of the following best describes the difference between $v$ (velocity) and $a$ (acceleration)?

• A. $v$ (velocity) describes the rate of change of position, while $a$ (acceleration) describes the rate of change of $v$ (velocity).
• B. $v$ (velocity) is always positive, while $a$ (acceleration) is always negative.
• C. $a$ (acceleration) is the total distance traveled, while $v$ (velocity) is the rate of change of $a$ (acceleration).
• D. $v$ (velocity) and $a$ (acceleration) both describe the rate of change of position.

Answer: (A)

Verified step by step guidance

1. Understand that velocity (\(v\)) is defined as the rate of change of position with respect to time. Mathematically, this is expressed as \(v = \frac{d x}{d t}\), where \(x\) is position and \(t\) is time.
2. Recognize that acceleration (\(a\)) is defined as the rate of change of velocity with respect to time. This can be written as \(a = \frac{d v}{d t}\).
3. Note that velocity can be positive or negative depending on the direction of motion, so it is a vector quantity that includes both magnitude and direction.
4. Similarly, acceleration can also be positive or negative, indicating whether the velocity is increasing or decreasing in a particular direction.
5. Summarize that velocity describes how position changes over time, while acceleration describes how velocity changes over time, making acceleration the derivative of velocity and velocity the derivative of position.