In introductory kinematics, which statement correctly distinguishes velocity from acceleration?

• A. Velocity and acceleration are the same quantity but expressed in different units.
• B. Velocity describes the rate of change of velocity with time, while acceleration describes the rate of change of position with time.
• C. Velocity is a scalar quantity, while acceleration is always a scalar quantity.
• D. Velocity describes the rate of change of position with time, while acceleration describes the rate of change of velocity with time.

Answer: (D)

Verified step by step guidance

1. Understand the definitions of velocity and acceleration in kinematics: Velocity is the rate of change of position with respect to time, and acceleration is the rate of change of velocity with respect to time.
2. Recall that velocity is a vector quantity, meaning it has both magnitude and direction, representing how fast and in which direction an object is moving.
3. Recognize that acceleration is also a vector quantity, indicating how the velocity of an object changes over time, including changes in speed or direction.
4. Identify that velocity is mathematically expressed as \(\\vec{v} = \\frac{d\\vec{x}}{dt}\), where \(\\vec{x}\) is position and \(t\) is time.
5. Identify that acceleration is mathematically expressed as \(\\vec{a} = \\frac{d\\vec{v}}{dt}\), where \(\\vec{v}\) is velocity and \(t\) is time.