The rate of change of velocity with time.
Explanation
In kinematics, the study of motion without considering its causes, physical quantities are defined to describe the movement of objects. Acceleration is a derived vector quantity that measures the variation in velocity over a specific duration.
Analysis of Options:
- The rate of change of position with time. is incorrect: The rate of change of position with respect to time is defined as velocity. It indicates the speed and direction of an object's displacement.
- The rate of change of velocity with time. is correct: Acceleration is defined as the rate of change of velocity with time. It quantifies how quickly an object speeds up, slows down, or changes its direction. Mathematically, instantaneous acceleration is expressed as a = dv/dt.
- The product of velocity and time. is incorrect: The product of velocity and time represents displacement (assuming uniform velocity). It indicates the change in position rather than the rate of change of motion.
- The ratio of total distance to total time. is incorrect: The ratio of total distance traveled to the total time taken is defined as average speed. Unlike acceleration, speed is a scalar quantity and does not account for direction.
Key Takeaway:
Acceleration is strictly the time rate of change of velocity. An object accelerates whenever its speed changes, its direction changes, or both change simultaneously.