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

• A. Velocity measures how far an object travels, while acceleration measures how long the motion takes.
• B. Velocity is the rate of change of position with time, while acceleration is the rate of change of velocity with time.
• C. Velocity is a scalar quantity, while acceleration is always a constant vector.
• D. Velocity is the rate of change of acceleration with time, while acceleration is the rate of change of position with time.

Answer: (B)

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 quickly and in what direction an object's position changes.
2. Step 2: Recognize that velocity is a vector quantity, meaning it has both magnitude (speed) and direction. This is important because direction affects how velocity changes.
3. Step 3: Understand acceleration as the rate of change of velocity with respect to time. Acceleration tells us how quickly the velocity of an object is changing, including changes in speed or direction.
4. Step 4: Note that acceleration is also a vector quantity, which means it can change the magnitude or direction of velocity, or both.
5. Step 5: Compare the given statements by checking if they correctly describe velocity as the rate of change of position and acceleration as the rate of change of velocity, both being vector quantities. The correct statement should reflect these fundamental definitions.