In introductory kinematics, which statement correctly describes the difference between velocity and acceleration?

• A. Velocity is the rate of change of position with time, while acceleration is the rate of change of velocity with time.
• B. Velocity is the rate of change of acceleration with time, while acceleration is the rate of change of position with time.
• C. Velocity and acceleration are the same quantity as long as the motion is in a straight line.
• D. Velocity is a scalar quantity and acceleration is always a scalar quantity.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the definitions of velocity and acceleration in kinematics. Velocity is defined as the rate of change of position with respect to time, which means it tells us how fast and in what direction an object is moving.
2. Step 2: Recognize that acceleration is defined as the rate of change of velocity with respect to time. This means acceleration describes how the velocity of an object changes over time, including changes in speed or direction.
3. Step 3: Note that velocity is a vector quantity because it has both magnitude (speed) and direction. Similarly, acceleration is also a vector quantity for the same reason.
4. Step 4: Compare the given statements by checking which correctly matches these definitions: velocity relates to position change over time, and acceleration relates to velocity change over time.
5. Step 5: Conclude that the correct statement is: 'Velocity is the rate of change of position with time, while acceleration is the rate of change of velocity with time.'